# Physics Worksheets - Page 3

Physics Worksheets
• Page 3
21.
The ordered pair notation of vector $\stackrel{\to }{\text{OM}}$ is
[Given $a$ = 21 and $b$ = 28.]

 a. <- 28, - 21> b. <- 21, - 28> c. <- 28, 21> d. <21, 28>

#### Solution:

As M is in quadrant III, the coordinates of M are (- 28, -21).
[From the figure.]

The ordered pair notation of vector OM is <- 28, -21>.

22.
Find the magnitude and direction of the vector $\stackrel{\to }{\text{OP}}$. [Given $b$ = 24 and $c$ = 7.]

 a. 25, tan-1($\frac{24}{7}$) west of north b. 24, north west c. 25, tan-1($\frac{24}{7}$) south of west d. 25, tan-1($\frac{24}{7}$) south of west

#### Solution:

In ΔOPM, OP = OM2 +PM2
[Pythagorean Theorem.]

OP = 72+242 = 25
[Substitute and simplify.]

tan θ = 24 / 7
[Use tangent ratio.]

θ = tan-1( 24 / 7)
[Find the angle.]

The magnitude and direction of vector OP are 25 and tan-1 (24 / 7) south of west.

23.
$\stackrel{\to }{\text{a}}$ = < 3, 5 >
$\stackrel{\to }{\text{b}}$ = < 5, 6 >
Find ($\stackrel{\to }{\text{a}}$ + $\stackrel{\to }{\text{b}}$)
.
 a. <8, 11> b. <11, - 8> c. <9, 10> d. <9, 11>

#### Solution:

a + b = <3, 5> + <5, 6>

= <3 + 5, 5 + 6>
[Add the x - coordinates and y - coordinates.]

= <8, 11>
[Simplify.]

24.
Which of the following is true?
 a. $\stackrel{\to }{\text{a}}$ - $\stackrel{\to }{\text{b}}$ = $\stackrel{\to }{\text{b}}$ - $\stackrel{\to }{\text{a}}$ b. $\stackrel{\to }{\text{a}}$ = -$\stackrel{\to }{\text{a}}$ c. $\stackrel{\to }{\text{a}}$ + $\stackrel{\to }{\text{b}}$ = $\stackrel{\to }{\text{b}}$ + $\stackrel{\to }{\text{a}}$ d. | $\stackrel{\to }{\text{a}}$ - $\stackrel{\to }{\text{b}}$| = | $\stackrel{\to }{\text{b}}$ + $\stackrel{\to }{\text{a}}$|

#### Solution:

By the parallelogram rule of vector addition, we have a + b = b + a.

25.
Which of the following is false?
 a. |$\stackrel{\to }{\text{v}}$| = | -$\stackrel{\to }{\text{v}}$| b. $\stackrel{\to }{\text{u}}$ + $\stackrel{\to }{\text{v}}$ = $\stackrel{\to }{\text{v}}$ + $\stackrel{\to }{\text{u}}$ c. $\stackrel{\to }{\text{a}}$ = - $\stackrel{\to }{\text{a}}$, $\stackrel{\to }{\text{a}}$ ≠ $\stackrel{\to }{\text{0}}$ d. | $\stackrel{\to }{\text{a}}$ - $\stackrel{\to }{\text{b}}$| = |$\stackrel{\to }{\text{b}}$ - $\stackrel{\to }{\text{a}}$|

#### Solution:

a and -a have same magnitude but opposite directions.

a ≠ -a
[a0.]

26.
Which of the following is true about $\stackrel{\to }{\text{OP}}$?
I) Direction of $\stackrel{\to }{\text{OP}}$ is 30° east of north
II) Direction of $\stackrel{\to }{\text{OP}}$ is 30° north of east
III) Direction of $\stackrel{\to }{\text{OP}}$ is 60° east of north
IV) Direction of $\stackrel{\to }{\text{OP}}$ is 60° north of east.

 a. I & IV b. I & II c. II & III d. II & IV

#### Solution:

The directions 30° north of east and 60° east of north are identical.

The direction of OP is 30° north of east and 60° east of north.