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Calculus 2 : Vector Form

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Example Questions

Example Question #91 : Vector Form

What is the vector form of -6i+j+k $\displaystyle -6i+j+k$ ?

Possible Answers:

$\left \langle -6,1,1\right \rangle$ $\displaystyle \left \langle -6,1,1\right \rangle$

$\left \langle -6,1,-1\right \rangle$ $\displaystyle \left \langle -6,1,-1\right \rangle$

$\left \langle 6,1,-1\right \rangle$ $\displaystyle \left \langle 6,1,-1\right \rangle$

$\left \langle 6,-1,1\right \rangle$ $\displaystyle \left \langle 6,-1,1\right \rangle$

$\left \langle 6,1,1\right \rangle$ $\displaystyle \left \langle 6,1,1\right \rangle$

Correct answer:

$\left \langle -6,1,1\right \rangle$ $\displaystyle \left \langle -6,1,1\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for -6i+j+k $\displaystyle -6i+j+k$ , we can derive the vector form $\left \langle -6,1,1\right \rangle$ $\displaystyle \left \langle -6,1,1\right \rangle$ .

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Example Question #91 : Vector Form

What is the vector form of 3i-k $\displaystyle 3i-k$ ?

Possible Answers:

$\left \langle 3,0,-1\right \rangle$ $\displaystyle \left \langle 3,0,-1\right \rangle$

$\left \langle 3,-1,0\right \rangle$ $\displaystyle \left \langle 3,-1,0\right \rangle$

$\left \langle -3,0,-1\right \rangle$ $\displaystyle \left \langle -3,0,-1\right \rangle$

$\left \langle 3,0,1\right \rangle$ $\displaystyle \left \langle 3,0,1\right \rangle$

$\left \langle -3,0,1\right \rangle$ $\displaystyle \left \langle -3,0,1\right \rangle$

Correct answer:

$\left \langle 3,0,-1\right \rangle$ $\displaystyle \left \langle 3,0,-1\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for 3i-k $\displaystyle 3i-k$ , we can derive the vector form $\left \langle 3,0,-1\right \rangle$ $\displaystyle \left \langle 3,0,-1\right \rangle$ .

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Example Question #223 : Ap Calculus Bc

Given points $\displaystyle (4,2,-2)$ and (7,1,0) $\displaystyle (7,1,0)$ , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle 3,-1,2\right \rangle$ $\displaystyle \left \langle 3,-1,2\right \rangle$

$\left \langle -3,1,-2\right \rangle$ $\displaystyle \left \langle -3,1,-2\right \rangle$

$\left \langle 3,1,2\right \rangle$ $\displaystyle \left \langle 3,1,2\right \rangle$

$\left \langle 3,1,-2\right \rangle$ $\displaystyle \left \langle 3,1,-2\right \rangle$

$\left \langle -3,1,2\right \rangle$ $\displaystyle \left \langle -3,1,2\right \rangle$

Correct answer:

$\left \langle 3,-1,2\right \rangle$ $\displaystyle \left \langle 3,-1,2\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

That is, for any point $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ and $b=\left \langle b_1,b_2,b_3\right \rangle$ , the distance is the vector $v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points $\displaystyle (4,2,-2)$ and (7,1,0) $\displaystyle (7,1,0)$ , we get:

$v=\left \langle 7-4,1-2,0-(-2)\right \rangle$ $\displaystyle v=\left \langle 7-4,1-2,0-(-2)\right \rangle$

$v=\left \langle 3,-1,2\right \rangle$ $\displaystyle v=\left \langle 3,-1,2\right \rangle$

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Example Question #91 : Vector Form

Given points $\displaystyle (2,7,-6)$ and (1,2,3) $\displaystyle (1,2,3)$ , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle 1,-5,-9\right \rangle$ $\displaystyle \left \langle 1,-5,-9\right \rangle$

$\left \langle -1,5,-9\right \rangle$ $\displaystyle \left \langle -1,5,-9\right \rangle$

$\left \langle -1,-5,-9\right \rangle$ $\displaystyle \left \langle -1,-5,-9\right \rangle$

$\left \langle -1,-5,9\right \rangle$ $\displaystyle \left \langle -1,-5,9\right \rangle$

$\left \langle 1,5,9\right \rangle$ $\displaystyle \left \langle 1,5,9\right \rangle$

Correct answer:

$\left \langle -1,-5,9\right \rangle$ $\displaystyle \left \langle -1,-5,9\right \rangle$

Explanation:

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points.

Subbing in our original points $\displaystyle (2,7,-6)$ and (1,2,3) $\displaystyle (1,2,3)$ , we get:

$v=\left \langle 1-2,2-7,3-(-6)\right \rangle$ $\displaystyle v=\left \langle 1-2,2-7,3-(-6)\right \rangle$

$v=\left \langle -1,-5,9\right \rangle$ $\displaystyle v=\left \langle -1,-5,9\right \rangle$

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Example Question #441 : Parametric, Polar, And Vector

What is the vector form of $\displaystyle -i+2j+10k$ ?

Possible Answers:

$\left \langle 1,2,-10\right \rangle$ $\displaystyle \left \langle 1,2,-10\right \rangle$

$\left \langle 1,2,10\right \rangle$ $\displaystyle \left \langle 1,2,10\right \rangle$

$\left \langle -1,2,10\right \rangle$ $\displaystyle \left \langle -1,2,10\right \rangle$

$\left \langle 1,-2,-10\right \rangle$ $\displaystyle \left \langle 1,-2,-10\right \rangle$

$\left \langle 1,-2,10\right \rangle$ $\displaystyle \left \langle 1,-2,10\right \rangle$

Correct answer:

$\left \langle -1,2,10\right \rangle$ $\displaystyle \left \langle -1,2,10\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for $\displaystyle -i+2j+10k$ , we can derive the vector form $\left \langle -1,2,10\right \rangle$ $\displaystyle \left \langle -1,2,10\right \rangle$ .

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Example Question #92 : Vector Form

What is the vector form of i+k $\displaystyle i+k$ ?

Possible Answers:

$\left \langle 1,1,0\right \rangle$ $\displaystyle \left \langle 1,1,0\right \rangle$

$\left \langle 0,1,1\right \rangle$ $\displaystyle \left \langle 0,1,1\right \rangle$

$\left \langle -1,0,1\right \rangle$ $\displaystyle \left \langle -1,0,1\right \rangle$

$\left \langle 1,0,-1\right \rangle$ $\displaystyle \left \langle 1,0,-1\right \rangle$

$\left \langle 1,0,1\right \rangle$ $\displaystyle \left \langle 1,0,1\right \rangle$

Correct answer:

$\left \langle 1,0,1\right \rangle$ $\displaystyle \left \langle 1,0,1\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for i+k $\displaystyle i+k$ , we can derive the vector form $\left \langle 1,0,1\right \rangle$ $\displaystyle \left \langle 1,0,1\right \rangle$ .

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Example Question #32 : Linear Algebra

What is the vector form of j+8k $\displaystyle j+8k$ ?

Possible Answers:

$\left \langle 0,1,8\right \rangle$ $\displaystyle \left \langle 0,1,8\right \rangle$

$\left \langle 0,8,1\right \rangle$ $\displaystyle \left \langle 0,8,1\right \rangle$

None of the above

$\left \langle 1,8,0\right \rangle$ $\displaystyle \left \langle 1,8,0\right \rangle$

$\left \langle 1,0,8\right \rangle$ $\displaystyle \left \langle 1,0,8\right \rangle$

Correct answer:

$\left \langle 0,1,8\right \rangle$ $\displaystyle \left \langle 0,1,8\right \rangle$

Explanation:

Given j+8k $\displaystyle j+8k$ , we need to map the $\displaystyle i$ , $\displaystyle j$ , and $\displaystyle k$ coefficients back to their corresponding $\displaystyle x$ , $\displaystyle y$ , and $\displaystyle z$ -coordinates.

Thus the vector form of j+8k $\displaystyle j+8k$ is $\left \langle 0,1,8\right \rangle$ $\displaystyle \left \langle 0,1,8\right \rangle$ .

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Example Question #31 : Linear Algebra

Express 4i-9j $\displaystyle 4i-9j$ in vector form.

Possible Answers:

$\left \langle 4,0,-9\right \rangle$ $\displaystyle \left \langle 4,0,-9\right \rangle$

$\left \langle 0,4,-9\right \rangle$ $\displaystyle \left \langle 0,4,-9\right \rangle$

$\left \langle 4,9,0\right \rangle$ $\displaystyle \left \langle 4,9,0\right \rangle$

$\left \langle 4,-9,0\right \rangle$ $\displaystyle \left \langle 4,-9,0\right \rangle$

$\left \langle 4,-9\right \rangle$ $\displaystyle \left \langle 4,-9\right \rangle$

Correct answer:

$\left \langle 4,-9,0\right \rangle$ $\displaystyle \left \langle 4,-9,0\right \rangle$

Explanation:

In order to express 4i-9j $\displaystyle 4i-9j$ in vector form, we must use the coefficients of i, j, $\displaystyle i, j,$ and $\displaystyle k$ to represent the $\displaystyle x$ -, $\displaystyle y$ -, and $\displaystyle z$ -coordinates of the vector.

Therefore, its vector form is

$\left \langle 4,-9,0\right \rangle$ $\displaystyle \left \langle 4,-9,0\right \rangle$ .

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Calculus 2 : Vector Form

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #91 : Vector Form

Example Question #91 : Vector Form

Example Question #223 : Ap Calculus Bc

Example Question #91 : Vector Form

Example Question #441 : Parametric, Polar, And Vector

Example Question #92 : Vector Form

Example Question #32 : Linear Algebra

Example Question #31 : Linear Algebra

All Calculus 2 Resources

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