10.4-10.5 Vectors Review
Work each problem out on a separate piece of notebook paper.
1. For each of the following vectors v, first, find the unit vector u that is in the same direction as v; then, find
the direction angle for v.
(a) v= -3, 7
(b) v= 4i + 9j
2. With the vectors v = -3i + 5j and w = 7i – 4j, find each part:
(a) 4v – 7w
(b) -2v + 5w
(c)
(d)
(e) the angle between v and w
3. With the vectors v = -4i – 6j and w = 8i – 4j, find each part:
(a) 4v – 7w
(b) -2v + 5w
(c)
(d)
4. The vector v is represented by the directed line segment
(a) R=(-4,3) and S=(5,-7)
(e) the angle between v and w
. Write v in the form ai + bj.
(b) R=(5,-2) and S=(-4,8)
5. Find whether the following vectors are orthogonal, parallel, or neither.
(a) v = 3i – 4j and w = -3i + 4j
(b) v = 3i – 2j and w = 4i + 6j
(c) v = -3i + 5j and w = 4i - 7j
6. Revisit Force problems - pg. 757 #64,71,72 – Know trig form
10.4-10.5 Vectors Review
Work each problem out on a separate piece of notebook paper.
1. For each of the following vectors v, first, find the unit vector u that is in the same direction as v; then, find
the direction angle for v.
(a) v= -3, 7
(b) v= 4i + 9j
2. With the vectors v = -3i + 5j and w = 7i – 4j, find each part:
(a) 4v – 7w
(b) -2v + 5w
(c)
(d)
(e) the angle between v and w
3. With the vectors v = -4i – 6j and w = 8i – 4j, find each part:
(a) 4v – 7w
(b) -2v + 5w
(c)
(d)
4. The vector v is represented by the directed line segment
(a) R=(-4,3) and S=(5,-7)
(e) the angle between v and w
. Write v in the form ai + bj.
(b) R=(5,-2) and S=(-4,8)
5. Find whether the following vectors are orthogonal, parallel, or neither.
(a) v = 3i – 4j and w = -3i + 4j
(b) v = 3i – 2j and w = 4i + 6j
6. Revisit Force problems - pg. 757 #64,71,72 – Know trig form
(c) v = -3i + 5j and w = 4i - 7j