XY-plane makes 45° with the X-axis.
a) F = 25 N
b) F = 25 2 N
c) F, = 25 N
Tatrix matching type.
For problem of Column I, a = 3i+4j,b=2î+2j-Ã and c = 3i
Column I
Column II
ne
a) 5
Ja+b
b)
3
a-c
c) 7.87
sb = 1, then s =
d) 42
Observe the figure and identify the correct options (MAQ)
Answers
Solutions to selected problems: Homework 1
Math 223 · Section 12 · Fall 2015 Dr. Gilbert
1. Find a vector of length 2 that points in the same direction as ˆi − ˆj + 2ˆk
Solution: Let ~v = ˆi−ˆj + 2ˆk. First, we can find a unit vector that points in the same direction
as ~v: We have
||~v|| =
p
1
2 + 12 + 22 =
√
6.
Thus, a unit vector pointing in the direction of ~v is given by
vˆ =
~v
||v|| =
1
√
6
ˆi −
1
√
6
ˆj +
2
√
6
ˆk.
To obtain the desired vector, we simply scale ˆv by a factor of 2:
~w = 2ˆv =
2
√
6
ˆi −
2
√
6
ˆj +
4
√
6
ˆk.
2. A particle moving with speed v hits a barrier at an angle of 60◦ and bounces off at an angle
of 60◦
in the opposite direction with speed reduced by 20%. See the figure below. Find the
velocity vector of the object after impact.
Solution: After impact, the speed of the particle is reduced by 20%. Therefore, since the
original speed was v, the final speed will be 0.8v. Using a little bit of trigonometry, and resolving
the final velocity vector, ~vf , into components, we get
~vf = 0.8v cos(π
3
)ˆi + 0.8v sin(π
3
)ˆj = 0.4vˆi + 0.4v
√
3ˆj.