Vector Practice Test 2 ( Addition & Resolution of Vector )

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1 / 29

If u·v = 0 (and neither u nor v is the zero vector), then u and v are:

A) Parallel

B) Perpendicular

C) Equal in length

D) One must be the zero vector

2 / 29

The vector from P(1, 2, 3) to Q(4, 0, 5) is:

A) 3i – 2j + 2k

B) – 3i + 2j – 2k

C) i + j + k

D) 4i + 0j + 5k

3 / 29

A unit vector u satisfies u×i = j. Then u is:

A) k

B) –k

C) j

D) –j

4 / 29

If u and v are two perpendicular unit vectors, then |u + v| equals:

A) 1

B) √2

C) 2

D) 0

5 / 29

Which property holds for any unit vector u?

A) u·u = 1

B) |u| = u

C) u×u = u

D) u + u = 1

6 / 29

The unit vector parallel to a = 3 i – 4 j + 12 k is:

A) (3/13) i – (4/13) j + (12/13) k

B) (3/5) i – (4/5) j + (12/5) k

C) (3/13) i + (4/13) j + (12/13) k

D) (–3/13) i + (4/13) j – (12/13) k

7 / 29

Which of the following is a unit vector?

A) i + j + k

B) ( i + j + k ) / √3

C) 2 i + 0 j + 0 k

D) i – k

8 / 29

A force of 25 N acts at 180° to the x-axis. What is the magnitude of its x-component?

A) 0 N

B) 12.5 N

C) 25 N

D) –25 N

9 / 29

A force of 8 N acts at 45° to the x-axis. What is the magnitude of its x-component?

A) 4 N

B) 4√2 N

C) 8 N

D) 0 N

10 / 29

A force of 12 N acts at 30° to the x-axis. What is the magnitude of its y-component?

A) 3 N

B) 6 N

C) 10 N

D) 12 N

11 / 29

A force of 15 N acts at 90° to the x-axis. What is the magnitude of its x-component?

A) 0 N

B) 7.5 N

C) 15 N

D) 30 N

12 / 29

A force of 20 N acts at 60° to the x-axis. What is the magnitude of its x-component?

A) 5 N

B) 10 N

C) 15 N

D) 20 N

13 / 29

A force of 10 N is acting along the x-axis. Which of the following is the magnitude of its y-component?

A) 1 N

B) 5 N

C) 15 N

D) 0 N

14 / 29

A force of 10 N is acting along the x-axis. Which of the following is the magnitude of its y-component?

A) 1 N

B) 10 N

C) 5 N

D) 0 N

15 / 29

For any nonzero scalar k, the vector kA is ______ to A.

A) parallel

B) perpendicular

C) identical

D) zero

16 / 29

The magnitude of the vector 3A is

A) 3|A|

B) |A|

C) |A|/3

D) 0

17 / 29

If a vector is multiplied by a scalar k then the resultant may be

A) 0

B) kA

C) –kA

D) all of these

18 / 29

Two vectors are said to be collinear if the angle between them is

A) 0° or 180°

B) 90°

C) 45°

D) undefined

19 / 29

The magnitude of the cross product A × B is given by

A) A + B

B) A B cos θ

C) A B sin θ

D) |A – B|

20 / 29

The vector having zero magnitude and arbitrary direction is called

A) zero vector

B) null vector

C) unit vector

D) both a & b

21 / 29

The cross product A × B of two parallel vectors is:

A) AB

B) 0

C) A – B

D) a vector perpendicular to both

22 / 29

The dot product A · B of two perpendicular vectors is:

A) AB

B) 0

C) A + B

D) √(A² + B²)

23 / 29

A unit vector is defined as a vector whose magnitude is:

A) 0

B) 1

C) equal to the magnitude of the original vector

D) greater than 1

24 / 29

Adding any vector A to the zero vector 0 gives:

A) A

B) 0

C) 2A

D) –A

25 / 29

If two perpendicular vectors of magnitudes A and B are added, the magnitude of the resultant R is:

A) A + B

B) A² + B²

C) √(A² + B²)

D) |A – B|

26 / 29

Vector addition is commutative. That means:

A) A + B ≠ B + A

B) (A + B) + C = A + (B + C)

C) A + B = B + A

D) A × B = B × A

27 / 29

Addition of vectors obey the law of _____

A) head-to-tail rule

B) simple addition

C) cross product

D) dot product

28 / 29

Two forces each of 10 N act at angles of 0° and 90° to the x-axis. What is the magnitude of their resultant?

A) 10 N

B) 14.14 N

C) 20 N

D) 0 N

29 / 29

A child pulls a box with a force of 200N at an angle of 60∘ above the horizontal. Then the horizontal and vertical components of the force will be:

A) 100N, 175 N

B) 86.6 N, 100N

C) 100 N, 86.6 N

D) 100 N, 0 N

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