# Physics Worksheets - Page 2

Physics Worksheets
• Page 2
11.
The direction of vector $\stackrel{\to }{\text{PQ}}$ is

 a. southeast b. southwest c. northwest d. northeast

#### Solution:

The direction of vector PQ is southwest or 45° south of west.
[From the figure.]

12.
Which of the following is a vector?
 a. Wind is blowing at 20 kmph, northwards. b. A man is traveling in northeast direction. c. A girl is running at 10 kmph. d. A car travels at 40 kmph

#### Solution:

A vector has both magnitude and direction.

The velocity of the wind in one of the options is a vector as both its magnitude and direction are given.

13.
Two vectors are said to be equal if they have the same ...
 a. magnitude b. direction and magnitude c. direction or magnitude d. direction

#### Solution:

Equal vectors have same direction and magnitude.

14.
The ordered pair notation of vector $\stackrel{\to }{\text{OP}}$ is ...

 a. <5, - 10> b. <5, 10> c. <10, 5> d. <-10, - 5>

#### Solution:

The coordinates of P are (10, 5).

The ordered pair notation of vector OP is <10, 5>.

15.
The ordered pair notation of $\stackrel{\to }{\text{OQ}}$ is [Given $a$ = 63.]

 a. < - 48.2, 40.4> b. < - 40.4, 48.2> c. <40.4, - 63> d. <63, 40.4>

#### Solution:

cos 50° = OM63 and sin 50° = QM63.
[Use sine and cosine.]

OM = 63 (cos 50°) and QM= 63 (sin 50°)
[Cross multiply.]

OM 40.4 and QM 48.2

As Q lies in the second quadrant, its y - coordinate is positive and x - coordinate is negative.

The coordinates of Q are (- 40.4, 48.2)

The ordered pair notation of OQ is < - 40.4, 48.2>

16.
Parallel vectors have same ...
 a. magnitude and direction b. direction c. magnitude

#### Solution:

Parallel vectors have same direction.

17.
A vector has ...
 a. both magnitude and direction. b. finite number of points. c. direction. d. magnitude.

#### Solution:

By definition, a vector is any quantity that has both magnitude and direction.

18.
The magnitude of vector $\stackrel{\to }{\text{AB}}$ is [Given $a$ = 5.]

 a. ± 5 b. - 5 c. 5 d. None of the above

#### Solution:

Magnitude of a vector can never be negative.

From the figure, magnitude of vector AB is 5.

19.
Which of the following vectors has a magnitude of 5 units?

 a. Figure D b. Figure B c. Figure A d. Figure C

#### Solution:

In figure D, OL = OK2 +KL2 = 32 +42= 5 units.
[Use Pythagorean Theorem and simplify.]

The magnitude of OL is 5 units.

20.
Which of the following vectors has the same magnitude as <27, 36>?
 a. <- 27, 36> b. <27, - 36> c. <- 27, - 36> d. All of the above

#### Solution:

The magnitude of the vector <x, y> is x2+y2

Magnitude of <27, 36> = 272+362 = 45.

Magnitude of <27, - 36> = 272+(-36)2 = 45.

Magnitude of <- {27], - 36> = (-27)2+(-36)2 = 45.

The vectors <27, 36>, < - 27, 36>, <27, - 36>, and < - 27, - 36> have the same magnitude.