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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 #2 : Vectors & Spaces

Assume that Billy fired himself out of a circus cannon at a velocity of $25 \:mph$ at an elevation angle of degrees. Write this in vector component form.

Possible Answers:

$\left \langle22.658,10.565 \right \rangle$

$\left \langle 25.25,25.25\right \rangle$

$\left \langle23.097, 9.567 \right \rangle$

$\left \langle 50,50\right \rangle$

$\left \langle 24.78,-3.309\right \rangle$

Correct answer:

$\left \langle22.658,10.565 \right \rangle$

Explanation:

The firing of the cannon has both x and y components.

Write the formula that distinguishes the x and y direction and substitute.

$\left \langle x,y\right \rangle= \left \langle vcos(\theta),vsin(\theta)\right \rangle$

Ensure that the calculator is in degree mode before you solve.

$\left \langle 25cos25,25sin25\right \rangle = \left \langle22.658,10.565 \right \rangle$

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Example Question #3 : Vectors & Spaces

Compute: $2\vec{a}-6\vec{b}$ given the following vectors. $\vec{a}= \left \langle 1,3\right \rangle$ and $\vec{b}= \left \langle 1\right \rangle$ .

Possible Answers:

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

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

${}\left< \sqrt{13} \right \rangle$

The answer does not exist.

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

Correct answer:

The answer does not exist.

Explanation:

The dimensions of the vectors are mismatched.

Since vector $\vec{a}$ does not have the same dimensions as $\vec{b}$ , the answer for $2\vec{a}-6\vec{b}$ cannot be solved.

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Example Question #1 : Vector Form

What is the vector form of 2i-10k ?

Possible Answers:

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

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

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

Correct answer:

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

Explanation:

To find the vector form of 2i-10k , we must map the coefficients of , , and to their corresponding , , and coordinates. Thus, 2i-10k becomes $\left \langle 2,0,-10\right \rangle$ .

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Example Question #1 : Vector Form

Express -2i+7j-10k in vector form.

Possible Answers:

$\left \langle 2,-7,10\right \rangle$

$\left \langle -2,-7,-10\right \rangle$

$\left \langle 2,7,-10\right \rangle$

$\left \langle -2,7,-10\right \rangle$

$\left \langle 2,7,10\right \rangle$

Correct answer:

$\left \langle -2,7,-10\right \rangle$

Explanation:

In order to express -2i+7j-10k in vector form, we must use the coefficients of i, j, and to represent the -, -, and -coordinates of the vector.

Therefore, its vector form is

$\left \langle -2,7,-10\right \rangle$ .

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Example Question #1 : Vector Form

Express i+5k in vector form.

Possible Answers:

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

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

$\left \langle -1,0,5\right \rangle$

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

$\left \langle 1,0,5\right \rangle$

Correct answer:

$\left \langle 1,0,5\right \rangle$

Explanation:

In order to express i+5k in vector form, we must use the coefficients of i, j, and to represent the -, -, and -coordinates of the vector.

Therefore, its vector form is

$\left \langle 1,0,5\right \rangle$ .

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Example Question #1 : Vector Form

Express -j+7k in vector form.

Possible Answers:

$\left \langle -1,7,0\right \rangle$

$\left \langle -1,0,7\right \rangle$

$\left \langle 0,-1,7\right \rangle$

None of the above

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

Correct answer:

$\left \langle 0,-1,7\right \rangle$

Explanation:

In order to express -j+7k in vector form, we will need to map its , , and coefficients to its -, -, and -coordinates.

Thus, its vector form is

$\left \langle 0,-1,7\right \rangle$ .

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Example Question #11 : Vector Form

Express 5i+9j-2k in vector form.

Possible Answers:

$\left \langle 5,9,-2\right \rangle$

$\left \langle 9,5,-2\right \rangle$

$\left \langle -2,5,9\right \rangle$

$\left \langle 9,-2,5\right \rangle$

None of the above

Correct answer:

$\left \langle 5,9,-2\right \rangle$

Explanation:

In order to express 5i+9j-2k in vector form, we will need to map its , , and coefficients to its -, -, and -coordinates.

Thus, its vector form is

$\left \langle 5,9,-2\right \rangle$ .

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Example Question #32 : Linear Algebra

Express -2i+3j in vector form.

Possible Answers:

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

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

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

None of the above

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

Correct answer:

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

Explanation:

In order to express -2i+3j in vector form, we will need to map its , , and coefficients to its -, -, and -coordinates.

Thus, its vector form is

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

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Example Question #11 : Vector Form

What is the vector form of 4i+4j-2k ?

Possible Answers:

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

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

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

None of the above

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

Correct answer:

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

Explanation:

To find the vector form of 4i+4j-2k , we must map the coefficients of , , and to their corresponding , , and coordinates.

Thus, 4i+4j-2k becomes $\left \langle 4,4,-2\right \rangle$ .

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Example Question #12 : Vector Form

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

Possible Answers:

None of the above

$\left \langle 0,-9,1\right \rangle$

$\left \langle 1,0,-9\right \rangle$

$\left \langle -9,0,1\right \rangle$

$\left \langle -9,1,0\right \rangle$

Correct answer:

$\left \langle 0,-9,1\right \rangle$

Explanation:

To find the vector form of -9j+k , we must map the coefficients of , , and to their corresponding , , and coordinates.

Thus, -9j+k becomes $\left \langle 0,-9,1\right \rangle$ .

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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 #2 : Vectors & Spaces

Example Question #3 : Vectors & Spaces

Example Question #1 : Vector Form

Example Question #1 : Vector Form

Example Question #1 : Vector Form

Example Question #1 : Vector Form

Example Question #11 : Vector Form

Example Question #32 : Linear Algebra

Example Question #11 : Vector Form

Example Question #12 : Vector Form

All Calculus 2 Resources

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