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Calculus 2 : Vector Form

Study concepts, example questions & explanations for Calculus 2

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9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #74 : Vectors

What is the vector form of $\displaystyle 4i-7j+2k$ ?

Possible Answers:

$\left \langle -4,-7,-2\right \rangle$ $\displaystyle \left \langle -4,-7,-2\right \rangle$

$\left \langle -4,7,-2\right \rangle$ $\displaystyle \left \langle -4,7,-2\right \rangle$

$\left \langle 4,7,2\right \rangle$ $\displaystyle \left \langle 4,7,2\right \rangle$

$\left \langle 4,-7,-2\right \rangle$ $\displaystyle \left \langle 4,-7,-2\right \rangle$

$\left \langle 4,-7,2\right \rangle$ $\displaystyle \left \langle 4,-7,2\right \rangle$

Correct answer:

$\left \langle 4,-7,2\right \rangle$ $\displaystyle \left \langle 4,-7,2\right \rangle$

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 $\displaystyle 4i-7j+2k$ , we can derive the vector form $\left \langle 4,-7,2\right \rangle$ $\displaystyle \left \langle 4,-7,2\right \rangle$ .

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Example Question #75 : Vectors

What is the vector form of $\displaystyle j$ ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $\displaystyle j$ , we can derive the vector form $\left \langle 0,1,0\right \rangle$ $\displaystyle \left \langle 0,1,0\right \rangle$ .

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Example Question #76 : Vectors

Given points $\displaystyle (5,2,-2)$ and (1,1,6) $\displaystyle (1,1,6)$ , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -4,-1,8\right \rangle$ $\displaystyle \left \langle -4,-1,8\right \rangle$

$\left \langle 4,1,8\right \rangle$ $\displaystyle \left \langle 4,1,8\right \rangle$

$\left \langle 4,-1,-8\right \rangle$ $\displaystyle \left \langle 4,-1,-8\right \rangle$

$\left \langle -4,-1,-8\right \rangle$ $\displaystyle \left \langle -4,-1,-8\right \rangle$

$\left \langle 4,-1,8\right \rangle$ $\displaystyle \left \langle 4,-1,8\right \rangle$

Correct answer:

$\left \langle -4,-1,8\right \rangle$ $\displaystyle \left \langle -4,-1,8\right \rangle$

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 $\displaystyle (5,2,-2)$ and (1,1,6) $\displaystyle (1,1,6)$ , we get:

$v=\left \langle 1-5,1-2,6-(-2)\right \rangle$ $\displaystyle v=\left \langle 1-5,1-2,6-(-2)\right \rangle$

$v=\left \langle -4,-1,8\right \rangle$ $\displaystyle v=\left \langle -4,-1,8\right \rangle$

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Example Question #77 : Vectors

Given points $\displaystyle (-7,0,5)$ and (0,4,2) $\displaystyle (0,4,2)$ , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle 7,-4,3\right \rangle$ $\displaystyle \left \langle 7,-4,3\right \rangle$

$\left \langle 7,4,-3\right \rangle$ $\displaystyle \left \langle 7,4,-3\right \rangle$

$\left \langle -7,-4,-3\right \rangle$ $\displaystyle \left \langle -7,-4,-3\right \rangle$

$\left \langle 7,-4,-3\right \rangle$ $\displaystyle \left \langle 7,-4,-3\right \rangle$

$\left \langle 7,4,3\right \rangle$ $\displaystyle \left \langle 7,4,3\right \rangle$

Correct answer:

$\left \langle 7,4,-3\right \rangle$ $\displaystyle \left \langle 7,4,-3\right \rangle$

Explanation:

Subbing in our original points $\displaystyle (-7,0,5)$ and (0,4,2) $\displaystyle (0,4,2)$ , we get:

$v=\left \langle 0-(-7),4-0,2-5\right \rangle$ $\displaystyle v=\left \langle 0-(-7),4-0,2-5\right \rangle$

$v=\left \langle 7,4,-3\right \rangle$ $\displaystyle v=\left \langle 7,4,-3\right \rangle$

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Example Question #272 : Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #273 : Algebra

What is the vector form of 7i+6j-k $\displaystyle 7i+6j-k$ ?

Possible Answers:

$\left \langle 7,-6,-1\right \rangle$ $\displaystyle \left \langle 7,-6,-1\right \rangle$

$\left \langle 7,6,-1\right \rangle$ $\displaystyle \left \langle 7,6,-1\right \rangle$

$\left \langle 7,6,1\right \rangle$ $\displaystyle \left \langle 7,6,1\right \rangle$

$\left \langle 7,-6,1\right \rangle$ $\displaystyle \left \langle 7,-6,1\right \rangle$

$\left \langle -7,-6,-1\right \rangle$ $\displaystyle \left \langle -7,-6,-1\right \rangle$

Correct answer:

$\left \langle 7,6,-1\right \rangle$ $\displaystyle \left \langle 7,6,-1\right \rangle$

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 7i+6j-k $\displaystyle 7i+6j-k$ , we can derive the vector form $\left \langle 7,6,-1\right \rangle$ $\displaystyle \left \langle 7,6,-1\right \rangle$ .

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Example Question #274 : Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #101 : Linear Algebra

Given points $\displaystyle (10,8,6)$ and $\displaystyle (7,9,11)$ , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -3,-1,-5\right \rangle$ $\displaystyle \left \langle -3,-1,-5\right \rangle$

$\left \langle 3,1,-5\right \rangle$ $\displaystyle \left \langle 3,1,-5\right \rangle$

$\left \langle 3,-1,5\right \rangle$ $\displaystyle \left \langle 3,-1,5\right \rangle$

$\left \langle -3,1,5\right \rangle$ $\displaystyle \left \langle -3,1,5\right \rangle$

$\left \langle 3,-1,-5\right \rangle$ $\displaystyle \left \langle 3,-1,-5\right \rangle$

Correct answer:

$\left \langle -3,1,5\right \rangle$ $\displaystyle \left \langle -3,1,5\right \rangle$

Explanation:

Subbing in our original points $\displaystyle (10,8,6)$ and $\displaystyle (7,9,11)$ , we get:

$v=\left \langle 7-10,9-8,11-6\right \rangle$ $\displaystyle v=\left \langle 7-10,9-8,11-6\right \rangle$

$v=\left \langle -3,1,5\right \rangle$ $\displaystyle v=\left \langle -3,1,5\right \rangle$

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Example Question #102 : Linear Algebra

Given points $\displaystyle (1,9,-1)$ and (2,2,7) $\displaystyle (2,2,7)$ , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle 1,7,-8\right \rangle$ $\displaystyle \left \langle 1,7,-8\right \rangle$

$\left \langle 1,-7,8\right \rangle$ $\displaystyle \left \langle 1,-7,8\right \rangle$

$\left \langle -1,-7,8\right \rangle$ $\displaystyle \left \langle -1,-7,8\right \rangle$

$\left \langle -1,7,8\right \rangle$ $\displaystyle \left \langle -1,7,8\right \rangle$

$\left \langle 1,7,8\right \rangle$ $\displaystyle \left \langle 1,7,8\right \rangle$

Correct answer:

$\left \langle 1,-7,8\right \rangle$ $\displaystyle \left \langle 1,-7,8\right \rangle$

Explanation:

Subbing in our original points $\displaystyle (1,9,-1)$ and (2,2,7) $\displaystyle (2,2,7)$ we get:

$v=\left \langle 2-1,2-9,7-(-1)\right \rangle$ $\displaystyle v=\left \langle 2-1,2-9,7-(-1)\right \rangle$

$v=\left \langle 1,-7,8\right \rangle$ $\displaystyle v=\left \langle 1,-7,8\right \rangle$

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Example Question #103 : Linear Algebra

What is the vector form of $\displaystyle 2i-18j+3k$ ?

Possible Answers:

$\left \langle 2,18,3\right \rangle$ $\displaystyle \left \langle 2,18,3\right \rangle$

$\left \langle 2,-18,3\right \rangle$ $\displaystyle \left \langle 2,-18,3\right \rangle$

$\left \langle -2,-18,-3\right \rangle$ $\displaystyle \left \langle -2,-18,-3\right \rangle$

$\left \langle 2,18,-3\right \rangle$ $\displaystyle \left \langle 2,18,-3\right \rangle$

$\left \langle -2,18,3\right \rangle$ $\displaystyle \left \langle -2,18,3\right \rangle$

Correct answer:

$\left \langle 2,-18,3\right \rangle$ $\displaystyle \left \langle 2,-18,3\right \rangle$

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 $\displaystyle 2i-18j+3k$ , we can derive the vector form $\left \langle 2,-18,3\right \rangle$ $\displaystyle \left \langle 2,-18,3\right \rangle$ .

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Calculus 2 : Vector Form

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #74 : Vectors

Example Question #75 : Vectors

Example Question #76 : Vectors

Example Question #77 : Vectors

Example Question #272 : Algebra

Example Question #273 : Algebra

Example Question #274 : Algebra

Example Question #101 : Linear Algebra

Example Question #102 : Linear Algebra

Example Question #103 : Linear Algebra

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