Download Pre-Calculus - MacPetersen

Review for Test 3-2
Precalculus
Vectors
Name: _____________________________
Round any degree measurements to the nearest whole degree.
1. Find the component form and the magnitude of vector v. Then write the vector as a linear
combination.
a.
b.
c.
2. Find the component form and the magnitude of vector v given the initial point (P) and the
terminal point (Q). Graph the vector in standard form (some may not fit on the graph). Finally,
write the vector as a linear combination.
a. P(-1,5) Q(15,12)
b. P(1,11) Q(9,3)
y
c. P(-3,-5) Q(5,1)
y
x
y
x
3. What are the requirements for two vectors to be considered equivalent?
x
4. Calculate the scalar products. Graph and label the resultant vectors.
y
a. 2<-1, 5>
b. 3<2, 3>
x
c. -1<6, 7>
d. - 23 <-3, 4>
5. Find u + v, u – v, and 4u – 2v.
a) u = <1 , 2>;
v = <3 , 1>
b) u = <3 , -2>;
v = <0 , -4>
c) u = i - j ;
v = 4i – j
d) u = -i + j ; v = -i + 3j
6. Find a unit vector in the direction of the given vector.
a) u = <0 , 3>
b) u = <3 , 3>
c) v = 3i - 4j
d) v = -3i + 2j
7. Use u =<3 , 3>, v = <-2 , 3>, and w = -2j to find the indicated quantity. Write vectors in
component form.
a. u  u
b. 2u  v
c. (u  v)v
d. (2v  u)w
e. ||w|| - ||u||
f. ||v|| + ||u||
g. (u  v) - (u  w)
h. (v  u) - (w  v)
i. The angle between u and v.
j. The angle between w and u.
8. Find u  v using the given information where  is the angle between u and v.
a. ||u|| = 5; ||v|| = 2;

= 32
b. ||u|| = 11; ||v|| = 20;  = 6
9. Determine whether u and v are orthogonal, parallel, or neither.
a. u = <-8 , 10>; v = < 23 ,  75 >
b. u = <25, -15>; v = <5 , -3>
c. u =
d. u = 3i + 3j; v = -2i + 2j
3
4
(3i – 4j); v = 2i + 6j
10. Find the magnitude and direction angle of the vector v.
a. v = <-4 , 5>
b. v = 4(cos 40o i + sin 40 o j)
11. Find the component form of vector v given its magnitude and direction angle.
a. ||v|| = 3,
 =30o
b. ||v|| = 1;  = in the direction of < −
√3
2
1
,2 >