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Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

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All Calculus 2 Resources

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

Example Questions

Example Question #91 : Linear Algebra

What is the vector form of ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #95 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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

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

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Example Question #91 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #92 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #93 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 , we can derive the vector form $\left \langle 7,6,-1\right \rangle$ .

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Example Question #71 : Vectors

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 , we can derive the vector form $\left \langle -1,1,1\right \rangle$ .

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Example Question #81 : Vectors & Spaces

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #76 : Vector Form

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #83 : Vectors & Spaces

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

Report an Error

Example Question #84 : Vectors & Spaces

What is the vector form of ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #91 : Linear Algebra

Example Question #95 : Linear Algebra

Example Question #91 : Linear Algebra

Example Question #92 : Linear Algebra

Example Question #93 : Linear Algebra

Example Question #71 : Vectors

Example Question #81 : Vectors & Spaces

Example Question #76 : Vector Form

Example Question #83 : Vectors & Spaces

Example Question #84 : Vectors & Spaces

All Calculus 2 Resources

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