Download Vectors Test Review

Pre Calculus
Unit 7 – Vectors
Unit Test REVIEW
Name _______________________________________
Date _____________________ Block ____________
𝑨 = < 𝟓, −𝟐 >
𝑯 = < 𝟐, 𝟐 >
𝑺 = < −𝟑, 𝟒 >
𝟑𝑯 + 𝟑𝑺
2.
1.
𝟐𝑨 – 𝑺
3.
𝟒𝑨 – 𝟑𝑯
4.
𝑨– 𝑯 + 𝑺
5.
____________ − 𝟐𝑨 = 𝑯
6.
𝑺 + ___________ = 𝟐𝑯
7.
‖𝑨‖
8.
‖𝑺‖
9.
What is the Direction Angle for vector 𝑯
10.
What is the Direction Angle for vector 𝑨
11.
Draw a sketch of vectors A, H and S in
standard position.
A
H
S
Graph each of the following on the given plane. Make sure you show your Resultant Vector
12) 2S + 2A
13) H – S
14) 2A – 3H + S
15) 2H + 2A – S
Show all work and round all answers to 2 decimal places.
17.
While flying due east at 120 km/h, an airplane is
also carried northward at 45 km/h by the wind
blowing due north. What is the plane’s resultant
velocity (Speed and Direction)?
18.
An airplane is traveling at a speed of 500 mph
with a bearing of N40oW at a fixed altitude and
no wind. As the plane crosses the Mississippi
river, it encounters a wind blowing with a
velocity of 50 mph in the direction of N20oE.
What is the resultant speed and direction of the
plane?
19.
A boat traveled south across a river at 12 miles
per hour. The current of the river is 5 miles per
hour 20o south of west, perpendicular to the
direction the boat is traveling. What is the
resultant vector (speed and direction) of the boat?
20.
A force of 100 lbs. makes an angle of 660 with a
second force. The resultant of the two forces
makes an angle of 32° with the first force. Find
the magnitude of the second force and the
resultant.
21.
Two forces are acting on an object. The first force,
F1 of 50 newtons, pulls at an angle of 400 north of
due west. The second force, F2 of 25 newtons,
pulls at an angle of 300 east of north. What is the
magnitude and direction of the resultant force on
the object?
22.
Two ships leave a port at the same time. The
direction of the first ship is N 73° E and the
direction of the second is S 65° E. If the ships
travel at the rate of 12 knots (1 knot = 1 nautical
mile per hour) and 15 knots, respectively,
determine how far apart they are after 2 hours
23.
A 10,000 pound object is suspended on a wire tied to two poles. The angle between the horizontal and the
wire to the shorter pole is 22o. The angle between the horizontal and the wire to the taller pole is 49 o. Find
the tension in the cable to each pole.