Find the vector equation for a line that passes through $P$ and intersects $L$
$begingroup$
I just need to know if my answer is right. If it isn't please tell me what the answer is and what I did wrong.
Question:
Let $L$ be the line with parametric equations
begin{align*}
x & = 5−t
\ y &= −10+2t
\ z & = −4−2t
end{align*}
Find the vector equation for a line that passes through the point $P=(3, −8, −5)$ and intersects L at a point that is distance 5 from the point $Q=(5, −10, −4)$. Note that there are two possible correct answers. Use the square root symbol '$sqrt{}$' where needed to give an exact value for your answer.
⟨x,y,z⟩=(?,?,?)+t⟨?,?,?⟩
My solution:
begin{align*}
a & = 5 - t
\ b & = -10 + 2t
\ c & = -4 -2t
\ (a-5)^2 + (b + 10)^2 + (c + 4)^2 & = 25
\ t^2 + 4t^2 + 4t^2 &= 25
\ t &= pm 5/3
\ a & = 5 pm 5/3
\ b & = -10 pm 10/3
\ c & = -4 pm 10/3
end{align*}
Answer: $langle x,y,zrangle = (3,-8,-5) + tlangle 2 pm 5/3, 2 pm 10/3, 1 pm 10/3rangle$
linear-algebra vector-spaces vectors linear-transformations vector-analysis
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
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add a comment |
$begingroup$
I just need to know if my answer is right. If it isn't please tell me what the answer is and what I did wrong.
Question:
Let $L$ be the line with parametric equations
begin{align*}
x & = 5−t
\ y &= −10+2t
\ z & = −4−2t
end{align*}
Find the vector equation for a line that passes through the point $P=(3, −8, −5)$ and intersects L at a point that is distance 5 from the point $Q=(5, −10, −4)$. Note that there are two possible correct answers. Use the square root symbol '$sqrt{}$' where needed to give an exact value for your answer.
⟨x,y,z⟩=(?,?,?)+t⟨?,?,?⟩
My solution:
begin{align*}
a & = 5 - t
\ b & = -10 + 2t
\ c & = -4 -2t
\ (a-5)^2 + (b + 10)^2 + (c + 4)^2 & = 25
\ t^2 + 4t^2 + 4t^2 &= 25
\ t &= pm 5/3
\ a & = 5 pm 5/3
\ b & = -10 pm 10/3
\ c & = -4 pm 10/3
end{align*}
Answer: $langle x,y,zrangle = (3,-8,-5) + tlangle 2 pm 5/3, 2 pm 10/3, 1 pm 10/3rangle$
linear-algebra vector-spaces vectors linear-transformations vector-analysis
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
$endgroup$
add a comment |
$begingroup$
I just need to know if my answer is right. If it isn't please tell me what the answer is and what I did wrong.
Question:
Let $L$ be the line with parametric equations
begin{align*}
x & = 5−t
\ y &= −10+2t
\ z & = −4−2t
end{align*}
Find the vector equation for a line that passes through the point $P=(3, −8, −5)$ and intersects L at a point that is distance 5 from the point $Q=(5, −10, −4)$. Note that there are two possible correct answers. Use the square root symbol '$sqrt{}$' where needed to give an exact value for your answer.
⟨x,y,z⟩=(?,?,?)+t⟨?,?,?⟩
My solution:
begin{align*}
a & = 5 - t
\ b & = -10 + 2t
\ c & = -4 -2t
\ (a-5)^2 + (b + 10)^2 + (c + 4)^2 & = 25
\ t^2 + 4t^2 + 4t^2 &= 25
\ t &= pm 5/3
\ a & = 5 pm 5/3
\ b & = -10 pm 10/3
\ c & = -4 pm 10/3
end{align*}
Answer: $langle x,y,zrangle = (3,-8,-5) + tlangle 2 pm 5/3, 2 pm 10/3, 1 pm 10/3rangle$
linear-algebra vector-spaces vectors linear-transformations vector-analysis
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
$endgroup$
I just need to know if my answer is right. If it isn't please tell me what the answer is and what I did wrong.
Question:
Let $L$ be the line with parametric equations
begin{align*}
x & = 5−t
\ y &= −10+2t
\ z & = −4−2t
end{align*}
Find the vector equation for a line that passes through the point $P=(3, −8, −5)$ and intersects L at a point that is distance 5 from the point $Q=(5, −10, −4)$. Note that there are two possible correct answers. Use the square root symbol '$sqrt{}$' where needed to give an exact value for your answer.
⟨x,y,z⟩=(?,?,?)+t⟨?,?,?⟩
My solution:
begin{align*}
a & = 5 - t
\ b & = -10 + 2t
\ c & = -4 -2t
\ (a-5)^2 + (b + 10)^2 + (c + 4)^2 & = 25
\ t^2 + 4t^2 + 4t^2 &= 25
\ t &= pm 5/3
\ a & = 5 pm 5/3
\ b & = -10 pm 10/3
\ c & = -4 pm 10/3
end{align*}
Answer: $langle x,y,zrangle = (3,-8,-5) + tlangle 2 pm 5/3, 2 pm 10/3, 1 pm 10/3rangle$
linear-algebra vector-spaces vectors linear-transformations vector-analysis
linear-algebra vector-spaces vectors linear-transformations vector-analysis
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
edited Jan 16 at 21:37
DreamVision2017
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
asked Jan 16 at 20:30
DreamVision2017DreamVision2017
318
318
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Your solution is correct. However, you may add a bit of explanation, e.g. "Let $(a,b,c)$ be the intersection point on $L$ with distance $5$ to $Q$. Then one has..."
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
Your solution is correct. However, you may add a bit of explanation, e.g. "Let $(a,b,c)$ be the intersection point on $L$ with distance $5$ to $Q$. Then one has..."
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
$endgroup$
add a comment |
$begingroup$
Your solution is correct. However, you may add a bit of explanation, e.g. "Let $(a,b,c)$ be the intersection point on $L$ with distance $5$ to $Q$. Then one has..."
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
$endgroup$
add a comment |
$begingroup$
Your solution is correct. However, you may add a bit of explanation, e.g. "Let $(a,b,c)$ be the intersection point on $L$ with distance $5$ to $Q$. Then one has..."
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
$endgroup$
Your solution is correct. However, you may add a bit of explanation, e.g. "Let $(a,b,c)$ be the intersection point on $L$ with distance $5$ to $Q$. Then one has..."
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
answered Jan 22 at 12:55
Jakob B.Jakob B.
527111
527111
add a comment |
add a comment |
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