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GRE Subject Test: Math : Vectors

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Example Questions

Example Question #71 : Linear Algebra

What is the vector form of i-3k $\displaystyle i-3k$ ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #72 : Linear Algebra

What is the vector form of 2i-j $\displaystyle 2i-j$ ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #241 : Algebra

Write the following parametric equation in vector form.

z=t^3s $\displaystyle z=t^3s$

x=0 $\displaystyle x=0$

y=s^2 $\displaystyle y=s^2$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

<x-component, y-component, z-component> $\displaystyle < x-component, y-component, z-component>$

Given the question

z=t^3s $\displaystyle z=t^3s$

x=0 $\displaystyle x=0$

y=s^2 $\displaystyle y=s^2$

the vector would be given as,

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

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Example Question #71 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #53 : Vectors & Spaces

What is the vector form of 4i+k $\displaystyle 4i+k$ ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #73 : Linear Algebra

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #51 : Vectors

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

Possible Answers:

-4i-3j $\displaystyle -4i-3j$

4i+3j $\displaystyle 4i+3j$

7i+3j $\displaystyle 7i+3j$

i+j $\displaystyle i+j$

Correct answer:

4i+3j $\displaystyle 4i+3j$

Explanation:

We must first find the vector in component form.

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

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

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

Hence, the vector in standard form is

4i+3j $\displaystyle 4i+3j$

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Example Question #52 : Vector Form

What is the vector form of $\displaystyle 3i-5j+7k$ ?

Possible Answers:

$\left \langle 3,-5,7\right \rangle$ $\displaystyle \left \langle 3,-5,7\right \rangle$

$\left \langle -3,-5,-7\right \rangle$ $\displaystyle \left \langle -3,-5,-7\right \rangle$

$\left \langle -3,-5,7\right \rangle$ $\displaystyle \left \langle -3,-5,7\right \rangle$

$\left \langle 3,5,-7\right \rangle$ $\displaystyle \left \langle 3,5,-7\right \rangle$

$\left \langle -3,5,7\right \rangle$ $\displaystyle \left \langle -3,5,7\right \rangle$

Correct answer:

$\left \langle 3,-5,7\right \rangle$ $\displaystyle \left \langle 3,-5,7\right \rangle$

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 $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ $\displaystyle a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for $\displaystyle 3i-5j+7k$ , we can derive the vector form $\left \langle 3,-5,7\right \rangle$ $\displaystyle \left \langle 3,-5,7\right \rangle$ .

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Example Question #432 : Gre Subject Test: Math

What is the vector form of $\displaystyle 7i$ ?

Possible Answers:

$\left \langle 0,0,7\right \rangle$ $\displaystyle \left \langle 0,0,7\right \rangle$

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

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

$\left \langle 7,0,0\right \rangle$ $\displaystyle \left \langle 7,0,0\right \rangle$

$\left \langle 0,7,0,\right \rangle$ $\displaystyle \left \langle 0,7,0,\right \rangle$

Correct answer:

$\left \langle 7,0,0\right \rangle$ $\displaystyle \left \langle 7,0,0\right \rangle$

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 $\displaystyle 7i$ , we can derive the vector form $\left \langle 7,0,0\right \rangle$ $\displaystyle \left \langle 7,0,0\right \rangle$ .

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Example Question #401 : Parametric, Polar, And Vector

Given points (9,4,-1) and (5,2,7) , what is the vector form of the distance between the points?

Possible Answers:

$\left \langle -4,2,8\right \rangle$ $\displaystyle \left \langle -4,2,8\right \rangle$

$\left \langle 4,-2,8\right \rangle$ $\displaystyle \left \langle 4,-2,8\right \rangle$

$\left \langle -4,-2,-8\right \rangle$ $\displaystyle \left \langle -4,-2,-8\right \rangle$

$\left \langle 4,2,8\right \rangle$ $\displaystyle \left \langle 4,2,8\right \rangle$

$\left \langle -4,-2,8\right \rangle$ $\displaystyle \left \langle -4,-2,8\right \rangle$

Correct answer:

$\left \langle -4,-2,8\right \rangle$ $\displaystyle \left \langle -4,-2,8\right \rangle$

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 $b=\left \langle b_1,b_2,b_3\right \rangle$ $\displaystyle b=\left \langle b_1,b_2,b_3\right \rangle$ ,

the distance is the vector

$v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ $\displaystyle v=\left \langle b_1-a_1,b_2-a_2,b_3-a_3\right \rangle$ .

Subbing in our original points (9,4,-1) and (5,2,7) , we get:

$v=\left \langle 5-9,2-4,7-(-1)\right \rangle$ $\displaystyle v=\left \langle 5-9,2-4,7-(-1)\right \rangle$

$v=\left \langle -4,-2,8\right \rangle$ $\displaystyle v=\left \langle -4,-2,8\right \rangle$

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GRE Subject Test: Math : Vectors

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

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

Example Question #52 : Vector Form

Example Question #432 : Gre Subject Test: Math

Example Question #401 : Parametric, Polar, And Vector

All GRE Subject Test: Math Resources

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