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1 Vectors for Engineering Mechanics Online Quiz Questions

Use this free practice quiz with 20 questions to review 1 Vectors for Engineering Mechanics, test your knowledge, and prepare for your next test or exam.

20 questions
01
True or false
1 point

If a vector is multiplied by a negative scalar, its direction reverses.

  1. A

    True

  2. B

    False

02
Choose one
1 point

A force of 20 N20\,\mathrm{N} acts at 30∘30^\circ counterclockwise from the positive xx-axis. Which expression gives its Cartesian vector components?

  1. A

    (103 i+10 j) N(10\sqrt{3}\,\mathbf{i}+10\,\mathbf{j})\,\mathrm{N}

  2. B

    (10 i+103 j) N(10\,\mathbf{i}+10\sqrt{3}\,\mathbf{j})\,\mathrm{N}

  3. C

    (−103 i+10 j) N(-10\sqrt{3}\,\mathbf{i}+10\,\mathbf{j})\,\mathrm{N}

  4. D

    (20 i+30 j) N(20\,\mathbf{i}+30\,\mathbf{j})\,\mathrm{N}

03
Fill in the blank
1 point

For P(1,2,0)P(1,2,0) and Q(4,−1,5)Q(4,-1,5), complete the components of PQ→\overrightarrow{PQ}: PQ→=\overrightarrow{PQ}=i+\mathbf{i}+j+\mathbf{j}+k\mathbf{k}.

04
Choose one
1 point

Given A⃗=5i−2j\vec A=5\mathbf{i}-2\mathbf{j} and B⃗=i+4j\vec B=\mathbf{i}+4\mathbf{j}, what is A⃗−B⃗\vec A-\vec B?

  1. A

    6i+2j6\mathbf{i}+2\mathbf{j}

  2. B

    4i+6j4\mathbf{i}+6\mathbf{j}

  3. C

    4i−6j4\mathbf{i}-6\mathbf{j}

  4. D

    6i−2j6\mathbf{i}-2\mathbf{j}

05
Written response
1 point

A vector has components (3,4,12)(3,4,12). What is its magnitude?

06
True or false
1 point

In a right-handed Cartesian coordinate system, each of i\mathbf{i}, j\mathbf{j}, and k\mathbf{k} has magnitude 1.

  1. A

    True

  2. B

    False

07
Choose all
1 point

Select all statements that are true about dot and cross products.

  1. A

    The dot product of two vectors is a scalar.

  2. B

    If two nonzero vectors have a dot product of zero, they are perpendicular.

  3. C

    The cross product of two vectors is always a scalar.

  4. D

    The magnitude of a cross product is ∣A⃗∣∣B⃗∣sin⁡ϕ|\vec A||\vec B|\sin\phi, where ϕ\phi is the angle between the vectors.

08
Fill in the blank
1 point

For a nonzero vector A⃗\vec A, the unit vector in its direction is .

09
Written response
1 point

For A⃗=(2,−1,3)\vec A=(2,-1,3) and B⃗=(4,5,2)\vec B=(4,5,2), what is A⃗⋅B⃗\vec A\cdot\vec B?

10
Choose one
1 point

In a right-handed Cartesian coordinate system, what is i×j\mathbf{i}\times\mathbf{j}?

  1. A

    −k-\mathbf{k}

  2. B

    k\mathbf{k}

  3. C

    i\mathbf{i}

  4. D

    −j-\mathbf{j}

11
Choose all
1 point

For A⃗=2i−3j+k\vec A=2\mathbf{i}-3\mathbf{j}+\mathbf{k}, select all statements that are true.

  1. A

    The scalar component AxA_x is 22.

  2. B

    −3j-3\mathbf{j} is a vector component of A⃗\vec A.

  3. C

    The scalar component AzA_z is −1-1.

  4. D

    k\mathbf{k} is the unit vector along the positive zz-axis.

12
Choose one
1 point

What is the magnitude of the vector A⃗=2i−3j+6k\vec A=2\mathbf{i}-3\mathbf{j}+6\mathbf{k}?

  1. A

    77

  2. B

    45\sqrt{45}

  3. C

    53\sqrt{53}

  4. D

    1111

13
Choose one
1 point

The vector A⃗=3i+4j\vec A=3\mathbf{i}+4\mathbf{j} points in a specified direction. What is the xx-component of the unit vector in that direction?

  1. A

    45\frac{4}{5}

  2. B

    34\frac{3}{4}

  3. C

    35\frac{3}{5}

  4. D

    15\frac{1}{5}

14
Open ended
1 point

A force F⃗=(4i−5j) N\vec F=(4\mathbf{i}-5\mathbf{j})\,\mathrm{N} is applied at a point whose position relative to the moment center is r⃗=(2i+3j) m\vec r=(2\mathbf{i}+3\mathbf{j})\,\mathrm{m}. Find the moment vector M⃗=r⃗×F⃗\vec M=\vec r\times\vec F.

15
True or false
1 point

In a Cartesian coordinate system, a negative scalar component of a vector means that component points opposite the positive direction of its axis.

  1. A

    True

  2. B

    False

16
Choose one
1 point

Given A⃗=2i−j\vec A=2\mathbf{i}-\mathbf{j} and B⃗=−i+3j\vec B=-\mathbf{i}+3\mathbf{j}, what is A⃗+B⃗\vec A+\vec B?

  1. A

    −i+2j-\mathbf{i}+2\mathbf{j}

  2. B

    i+2j\mathbf{i}+2\mathbf{j}

  3. C

    i−4j\mathbf{i}-4\mathbf{j}

  4. D

    3i+2j3\mathbf{i}+2\mathbf{j}

17
Written response
1 point

What kind of quantity does the dot product of two vectors produce?

18
Choose one
1 point

A force of magnitude 10 N10\,\mathrm{N} is directed 60∘60^\circ counterclockwise from the positive xx-axis. Which expression gives its components in unit-vector notation?

  1. A

    (5i+53j) N(5\mathbf{i}+5\sqrt{3}\mathbf{j})\,\mathrm{N}

  2. B

    (53i+5j) N(5\sqrt{3}\mathbf{i}+5\mathbf{j})\,\mathrm{N}

  3. C

    (10i+10j) N(10\mathbf{i}+10\mathbf{j})\,\mathrm{N}

  4. D

    (−5i+53j) N(-5\mathbf{i}+5\sqrt{3}\mathbf{j})\,\mathrm{N}

19
Written response
1 point

For A⃗=2i−j+3k\vec A=2\mathbf{i}-\mathbf{j}+3\mathbf{k} and B⃗=i+4j−2k\vec B=\mathbf{i}+4\mathbf{j}-2\mathbf{k}, what is the numerical value of A⃗⋅B⃗\vec A\cdot\vec B?

20
Choose one
1 point

Let A⃗=i−2j\vec A=\mathbf{i}-2\mathbf{j}. When A⃗\vec A is multiplied by the scalar −3-3, which statement describes the resulting vector?

  1. A

    Magnitude 5\sqrt{5}, with the same direction as A⃗\vec A

  2. B

    Magnitude 353\sqrt{5}, with the same direction as A⃗\vec A

  3. C

    Magnitude 353\sqrt{5}, with the direction opposite to A⃗\vec A

  4. D

    Magnitude 959\sqrt{5}, with the direction opposite to A⃗\vec A