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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 #41 : Vector Form

What is the vector form of -j+4k ?

Possible Answers:

$\left \langle 0,1,4\right \rangle$

$\left \langle 1,0,-4\right \rangle$

$\left \langle 0,-1,4\right \rangle$

$\left \langle 0,-1,-4\right \rangle$

$\left \langle 0,1,-4\right \rangle$

Correct answer:

$\left \langle 0,-1,4\right \rangle$

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 -j+4k , we can derive the vector form $a=\left \langle 0,-1,4\right \rangle$ .

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Example Question #42 : Vectors

What is the vector form of 2i+10j ?

Possible Answers:

$\left \langle 2,-10,0\right \rangle$

$\left \langle 2,10,0\right \rangle$

$\left \langle -2,10,0\right \rangle$

$\left \langle -2,-10,0\right \rangle$

$\left \langle 0,2,10\right \rangle$

Correct answer:

$\left \langle 2,10,0\right \rangle$

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 2i+10j , we can derive the vector form $a=\left \langle 2,10,0\right \rangle$ .

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Example Question #42 : Vector Form

What is the vector form of -8i+8j-k ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 -8i+8j-k , we can derive the vector form $\left \langle -8,8,-1\right \rangle$ .

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Example Question #44 : Vector Form

What is the vector form of 7i+2j-7k ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #43 : Vector Form

What is the vector form of i-10j ?

Possible Answers:

$\left \langle 1,-10,0\right \rangle$

$\left \langle 0,1,-10\right \rangle$

$\left \langle 1,10,0\right \rangle$

$\left \langle 1,0,-10\right \rangle$

$\left \langle -1,10,0\right \rangle$

Correct answer:

$\left \langle 1,-10,0\right \rangle$

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 i-10j , we can derive the vector form $\left \langle 1,-10,0\right \rangle$ .

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Example Question #44 : Vector Form

What is the vector form of -i+9j+3k ?

Possible Answers:

$\left \langle 1,-9,-3\right \rangle$

$\left \langle -1,9,3\right \rangle$

$\left \langle -1,-9,-3\right \rangle$

$\left \langle 1,-9,3\right \rangle$

$\left \langle 1,9,-3\right \rangle$

Correct answer:

$\left \langle -1,9,3\right \rangle$

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 -i+9j+3k , we can derive the vector form $\left \langle -1,9,3\right \rangle$ .

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Example Question #71 : Linear Algebra

What is the vector form of i-3k ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #72 : Linear Algebra

What is the vector form of 2i-j ?

Possible Answers:

$\left \langle 2,1,0\right \rangle$

$\left \langle 0,-2,1\right \rangle$

$\left \langle -2,1,0\right \rangle$

$\left \langle -2,-1,0\right \rangle$

$\left \langle 2,-1,0\right \rangle$

Correct answer:

$\left \langle 2,-1,0\right \rangle$

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 2i-j , we can derive the vector form $\left \langle 2,-1,0\right \rangle$ .

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Example Question #51 : Vectors & Spaces

Write the following parametric equation in vector form.

z=t^3s

x=0

y=s^2

Possible Answers:

$\left<0,t^3s, s^2\right>$

$\left<s^2, t^3s,0\right>$

$\left<0, s^2, x^3y\right>$

$\left<0,s^2,t^3s\right>$

Correct answer:

$\left<0,s^2,t^3s\right>$

Explanation:

When converting parametric equations to vector valued functions, remember that the order of vectors goes as follows.

<x-component, y-component, z-component>

Given the question

z=t^3s

x=0

y=s^2

the vector would be given as,

$\left<0, s^2, t^3s\right>$ .

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Example Question #71 : Linear Algebra

What is the vector form of 10i-9j+8k ?

Possible Answers:

$\left \langle -10,-9,-8\right \rangle$

$\left \langle 10,-9,8\right \rangle$

$\left \langle 10,9,-8\right \rangle$

$\left \langle -10,9,8\right \rangle$

$\left \langle -10,9,-8\right \rangle$

Correct answer:

$\left \langle 10,-9,8\right \rangle$

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 10i-9j+8k , we can derive the vector form $\left \langle 10,-9,8\right \rangle$ .

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Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #41 : Vector Form

Example Question #42 : Vectors

Example Question #42 : Vector Form

Example Question #44 : Vector Form

Example Question #43 : Vector Form

Example Question #44 : Vector Form

Example Question #71 : Linear Algebra

Example Question #72 : Linear Algebra

Example Question #51 : Vectors & Spaces

Example Question #71 : Linear Algebra

All Calculus 2 Resources

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