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Calculus 2 : Parametric, Polar, and Vector

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

Example Questions

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 #241 : Algebra

Write the following parametric equation in vector form.

z=t^3s

x=0

y=s^2

Possible Answers:

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

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

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

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

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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Example Question #53 : Vectors & Spaces

What is the vector form of 4i+k ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 4i+k , we can derive the vector form $\left \langle 4,0,1\right \rangle$ .

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Example Question #73 : Linear Algebra

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

Possible Answers:

$\left \langle 0,2,-3\right \rangle$

$\left \langle 2,3,0\right \rangle$

$\left \langle- 2,3,0\right \rangle$

$\left \langle- 2,-3,0\right \rangle$

$\left \langle 2,-3,0\right \rangle$

Correct answer:

$\left \langle 2,-3,0\right \rangle$

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-3j , we can derive the vector form $\left \langle 2,-3,0\right \rangle$ .

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Example Question #51 : Vectors

Find the vector in standard form if the initial point is located at (3,7) and the terminal point is located at (7,10) .

Possible Answers:

-4i-3j

4i+3j

7i+3j

i+j

Correct answer:

4i+3j

Explanation:

We must first find the vector in component form.

If the initial point is (p_1,p_2) and the terminal point is (q_1,q_2) then the component form of the vector is $\left<q_1-p_1,q_2-p_2\right>$ .

As such, the component form of the vector in the problem is $\left<7-3,10-7\right>$ $=\left<4,3\right>$

Next, any vector with component form $\left<a,b\right>$ can be written in standard form as ai+bj .

Hence, the vector in standard form is

4i+3j

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Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

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 #241 : Algebra

Example Question #71 : Linear Algebra

Example Question #53 : Vectors & Spaces

Example Question #73 : Linear Algebra

Example Question #51 : Vectors

All Calculus 2 Resources

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