How the dot product of two vectors can be zero?












0












$begingroup$


I am given,



$vec s$$=2hat i+hat j-3hat k$



and



$vec r$$=4hat i+hat j+3hat k$



Now I am asked to calculate the dot product $vec scdotvec r$
But I am getting $0$ as result.



Is this possible? And if possible, then how can the dot product simply become zero?






vectors







share|cite|improve this question











$endgroup$








  • 5




    $begingroup$
    "When I add the component parts" Why are you adding the component parts? $langle 2,1,-3rangle$ is not the zero vector $langle 0,0,0rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:43






  • 3




    $begingroup$
    "Is this possible (to do a dot product with a zero vector)? How can I calculate it?" Regardless of what the entries are, you have $langle a_1,a_2,dots,a_nrangle cdot langle b_1,b_2,dots,b_nrangle = a_1b_1 + a_2b_2 + dots + a_nb_n$. Further, if a vector is actually a zero vector (i.e. every entry is zero) you should see quickly that any dot product involving it will equal zero. In your case, you are asked to calculate $langle 2,1,-3rangle cdot langle 4,1,3rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:46












  • $begingroup$
    Dot product zero iff vectors orthogonal.
    $endgroup$
    – coffeemath
    Jan 1 at 17:50
















0












$begingroup$


I am given,



$vec s$$=2hat i+hat j-3hat k$



and



$vec r$$=4hat i+hat j+3hat k$



Now I am asked to calculate the dot product $vec scdotvec r$
But I am getting $0$ as result.



Is this possible? And if possible, then how can the dot product simply become zero?






vectors







share|cite|improve this question











$endgroup$








  • 5




    $begingroup$
    "When I add the component parts" Why are you adding the component parts? $langle 2,1,-3rangle$ is not the zero vector $langle 0,0,0rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:43






  • 3




    $begingroup$
    "Is this possible (to do a dot product with a zero vector)? How can I calculate it?" Regardless of what the entries are, you have $langle a_1,a_2,dots,a_nrangle cdot langle b_1,b_2,dots,b_nrangle = a_1b_1 + a_2b_2 + dots + a_nb_n$. Further, if a vector is actually a zero vector (i.e. every entry is zero) you should see quickly that any dot product involving it will equal zero. In your case, you are asked to calculate $langle 2,1,-3rangle cdot langle 4,1,3rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:46












  • $begingroup$
    Dot product zero iff vectors orthogonal.
    $endgroup$
    – coffeemath
    Jan 1 at 17:50














0












0








0





$begingroup$


I am given,



$vec s$$=2hat i+hat j-3hat k$



and



$vec r$$=4hat i+hat j+3hat k$



Now I am asked to calculate the dot product $vec scdotvec r$
But I am getting $0$ as result.



Is this possible? And if possible, then how can the dot product simply become zero?






vectors







share|cite|improve this question











$endgroup$




I am given,



$vec s$$=2hat i+hat j-3hat k$



and



$vec r$$=4hat i+hat j+3hat k$



Now I am asked to calculate the dot product $vec scdotvec r$
But I am getting $0$ as result.



Is this possible? And if possible, then how can the dot product simply become zero?






vectors




vectors






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 1 at 18:23









amWhy

192k28225439




192k28225439










asked Jan 1 at 17:42









RocketKangarooRocketKangaroo

334




334








  • 5




    $begingroup$
    "When I add the component parts" Why are you adding the component parts? $langle 2,1,-3rangle$ is not the zero vector $langle 0,0,0rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:43






  • 3




    $begingroup$
    "Is this possible (to do a dot product with a zero vector)? How can I calculate it?" Regardless of what the entries are, you have $langle a_1,a_2,dots,a_nrangle cdot langle b_1,b_2,dots,b_nrangle = a_1b_1 + a_2b_2 + dots + a_nb_n$. Further, if a vector is actually a zero vector (i.e. every entry is zero) you should see quickly that any dot product involving it will equal zero. In your case, you are asked to calculate $langle 2,1,-3rangle cdot langle 4,1,3rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:46












  • $begingroup$
    Dot product zero iff vectors orthogonal.
    $endgroup$
    – coffeemath
    Jan 1 at 17:50














  • 5




    $begingroup$
    "When I add the component parts" Why are you adding the component parts? $langle 2,1,-3rangle$ is not the zero vector $langle 0,0,0rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:43






  • 3




    $begingroup$
    "Is this possible (to do a dot product with a zero vector)? How can I calculate it?" Regardless of what the entries are, you have $langle a_1,a_2,dots,a_nrangle cdot langle b_1,b_2,dots,b_nrangle = a_1b_1 + a_2b_2 + dots + a_nb_n$. Further, if a vector is actually a zero vector (i.e. every entry is zero) you should see quickly that any dot product involving it will equal zero. In your case, you are asked to calculate $langle 2,1,-3rangle cdot langle 4,1,3rangle$.
    $endgroup$
    – JMoravitz
    Jan 1 at 17:46












  • $begingroup$
    Dot product zero iff vectors orthogonal.
    $endgroup$
    – coffeemath
    Jan 1 at 17:50








5




5




$begingroup$
"When I add the component parts" Why are you adding the component parts? $langle 2,1,-3rangle$ is not the zero vector $langle 0,0,0rangle$.
$endgroup$
– JMoravitz
Jan 1 at 17:43




$begingroup$
"When I add the component parts" Why are you adding the component parts? $langle 2,1,-3rangle$ is not the zero vector $langle 0,0,0rangle$.
$endgroup$
– JMoravitz
Jan 1 at 17:43




3




3




$begingroup$
"Is this possible (to do a dot product with a zero vector)? How can I calculate it?" Regardless of what the entries are, you have $langle a_1,a_2,dots,a_nrangle cdot langle b_1,b_2,dots,b_nrangle = a_1b_1 + a_2b_2 + dots + a_nb_n$. Further, if a vector is actually a zero vector (i.e. every entry is zero) you should see quickly that any dot product involving it will equal zero. In your case, you are asked to calculate $langle 2,1,-3rangle cdot langle 4,1,3rangle$.
$endgroup$
– JMoravitz
Jan 1 at 17:46






$begingroup$
"Is this possible (to do a dot product with a zero vector)? How can I calculate it?" Regardless of what the entries are, you have $langle a_1,a_2,dots,a_nrangle cdot langle b_1,b_2,dots,b_nrangle = a_1b_1 + a_2b_2 + dots + a_nb_n$. Further, if a vector is actually a zero vector (i.e. every entry is zero) you should see quickly that any dot product involving it will equal zero. In your case, you are asked to calculate $langle 2,1,-3rangle cdot langle 4,1,3rangle$.
$endgroup$
– JMoravitz
Jan 1 at 17:46














$begingroup$
Dot product zero iff vectors orthogonal.
$endgroup$
– coffeemath
Jan 1 at 17:50




$begingroup$
Dot product zero iff vectors orthogonal.
$endgroup$
– coffeemath
Jan 1 at 17:50










1 Answer
1






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oldest

votes


















1












$begingroup$

$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
that means $vec s$ and $vec r$ are perpendicular to each other.the intuition behind this dot product is what amount of $vec s$ is working along with $vec r$?If we would get some positive value,then that would mean that there is some component of s along r as it brings us in a conclusion that s would be inclined to r.But we have a zero here,that means no component of s is working along r.it is only possible when vectors are orthogonal.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thank you, that explains the above comments and helps a lot!
    $endgroup$
    – RocketKangaroo
    Jan 1 at 17:55











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1 Answer
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$begingroup$

$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
that means $vec s$ and $vec r$ are perpendicular to each other.the intuition behind this dot product is what amount of $vec s$ is working along with $vec r$?If we would get some positive value,then that would mean that there is some component of s along r as it brings us in a conclusion that s would be inclined to r.But we have a zero here,that means no component of s is working along r.it is only possible when vectors are orthogonal.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thank you, that explains the above comments and helps a lot!
    $endgroup$
    – RocketKangaroo
    Jan 1 at 17:55
















1












$begingroup$

$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
that means $vec s$ and $vec r$ are perpendicular to each other.the intuition behind this dot product is what amount of $vec s$ is working along with $vec r$?If we would get some positive value,then that would mean that there is some component of s along r as it brings us in a conclusion that s would be inclined to r.But we have a zero here,that means no component of s is working along r.it is only possible when vectors are orthogonal.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thank you, that explains the above comments and helps a lot!
    $endgroup$
    – RocketKangaroo
    Jan 1 at 17:55














1












1








1





$begingroup$

$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
that means $vec s$ and $vec r$ are perpendicular to each other.the intuition behind this dot product is what amount of $vec s$ is working along with $vec r$?If we would get some positive value,then that would mean that there is some component of s along r as it brings us in a conclusion that s would be inclined to r.But we have a zero here,that means no component of s is working along r.it is only possible when vectors are orthogonal.






share|cite|improve this answer











$endgroup$



$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
that means $vec s$ and $vec r$ are perpendicular to each other.the intuition behind this dot product is what amount of $vec s$ is working along with $vec r$?If we would get some positive value,then that would mean that there is some component of s along r as it brings us in a conclusion that s would be inclined to r.But we have a zero here,that means no component of s is working along r.it is only possible when vectors are orthogonal.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Jan 1 at 18:38









J.G.

24.6k22539




24.6k22539










answered Jan 1 at 17:53









Rakibul Islam PrinceRakibul Islam Prince

1,010211




1,010211












  • $begingroup$
    Thank you, that explains the above comments and helps a lot!
    $endgroup$
    – RocketKangaroo
    Jan 1 at 17:55


















  • $begingroup$
    Thank you, that explains the above comments and helps a lot!
    $endgroup$
    – RocketKangaroo
    Jan 1 at 17:55
















$begingroup$
Thank you, that explains the above comments and helps a lot!
$endgroup$
– RocketKangaroo
Jan 1 at 17:55




$begingroup$
Thank you, that explains the above comments and helps a lot!
$endgroup$
– RocketKangaroo
Jan 1 at 17:55


















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