How the dot product of two vectors can be zero?
$begingroup$
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
edited Jan 1 at 18:23
amWhy
192k28225439
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
$endgroup$
add a comment |
$begingroup$
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
edited Jan 1 at 18:23
amWhy
192k28225439
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
$endgroup$
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
add a comment |
$begingroup$
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
edited Jan 1 at 18:23
amWhy
192k28225439
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
$endgroup$
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
edited Jan 1 at 18:23
amWhy
192k28225439
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
edited Jan 1 at 18:23
amWhy
192k28225439
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
edited Jan 1 at 18:23
amWhy
192k28225439
edited Jan 1 at 18:23
amWhy
192k28225439
edited Jan 1 at 18:23
amWhy
192k28225439
192k28225439
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
asked Jan 1 at 17:42
RocketKangarooRocketKangaroo
334
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
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.
edited Jan 1 at 18:38
J.G.
24.6k22539
answered Jan 1 at 17:53
Rakibul Islam PrinceRakibul Islam Prince
1,010211
$endgroup$
$begingroup$
Thank you, that explains the above comments and helps a lot!
$endgroup$
– RocketKangaroo
Jan 1 at 17:55
add a comment |
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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.
edited Jan 1 at 18:38
J.G.
24.6k22539
answered Jan 1 at 17:53
Rakibul Islam PrinceRakibul Islam Prince
1,010211
$endgroup$
$begingroup$
Thank you, that explains the above comments and helps a lot!
$endgroup$
– RocketKangaroo
Jan 1 at 17:55
add a comment |
$begingroup$
$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
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.
edited Jan 1 at 18:38
J.G.
24.6k22539
answered Jan 1 at 17:53
Rakibul Islam PrinceRakibul Islam Prince
1,010211
$endgroup$
$begingroup$
Thank you, that explains the above comments and helps a lot!
$endgroup$
– RocketKangaroo
Jan 1 at 17:55
add a comment |
$begingroup$
$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
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.
edited Jan 1 at 18:38
J.G.
24.6k22539
answered Jan 1 at 17:53
Rakibul Islam PrinceRakibul Islam Prince
1,010211
$endgroup$
$$vec s.vec r=(2hat i+hat j-3hat k)cdot(4hat i+hat j+3hat k)=8+1-9=0$$
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.
edited Jan 1 at 18:38
J.G.
24.6k22539
answered Jan 1 at 17:53
Rakibul Islam PrinceRakibul Islam Prince
1,010211
edited Jan 1 at 18:38
J.G.
24.6k22539
edited Jan 1 at 18:38
J.G.
24.6k22539
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
answered Jan 1 at 17:53
Rakibul Islam PrinceRakibul Islam Prince
1,010211
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
add a comment |
$begingroup$
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
add a comment |
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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