Find u + v, u – v, and 3u – 4v. Then sketch each resultant vector. (0, -6), v = (1, –2) u = (a) u + v u + v = y 2 y 2 -6 -4 -2 4 -6 -4 -2 2 4 -2 u -4 V -8 u + v u + v -10 - 10 y 10 y 10 u + V u+ v V u u X 6 -4 -2 2 6 -4 -2 2 6 -5 -5- (b) u - v u - v = y y 6 6 4 2 -6 -4 -2 4 6. -6 -4 -2 4 -2 u u – v u- v -4 -v -v -6 – 6 -8 y 81 y 81 6 -v -v 4 4 u – v u u- v 2 - 6 -4 -2 2 4 - 6 -4 -2 2 4 -2 -2 -4 -4 (c) 3u – 4v 3u – 4v = y y 20 20 10 10 - 20 - 10 10 20 - 20 -10 10 20 3u 3 u 3u – 4v - 10 - 10 3 u – 4 v -4v -4 v -20f - 20 y y 20 20 -4v -4v 10 3u – 4v 10 3u – 4v 3u 3u - 20 -10 10 20 - 20 -10 10 20 - 10 - 10 - 20 - 20아
Find u + v, u – v, and 3u – 4v. Then sketch each resultant vector. (0, -6), v = (1, –2) u = (a) u + v u + v = y 2 y 2 -6 -4 -2 4 -6 -4 -2 2 4 -2 u -4 V -8 u + v u + v -10 - 10 y 10 y 10 u + V u+ v V u u X 6 -4 -2 2 6 -4 -2 2 6 -5 -5- (b) u - v u - v = y y 6 6 4 2 -6 -4 -2 4 6. -6 -4 -2 4 -2 u u – v u- v -4 -v -v -6 – 6 -8 y 81 y 81 6 -v -v 4 4 u – v u u- v 2 - 6 -4 -2 2 4 - 6 -4 -2 2 4 -2 -2 -4 -4 (c) 3u – 4v 3u – 4v = y y 20 20 10 10 - 20 - 10 10 20 - 20 -10 10 20 3u 3 u 3u – 4v - 10 - 10 3 u – 4 v -4v -4 v -20f - 20 y y 20 20 -4v -4v 10 3u – 4v 10 3u – 4v 3u 3u - 20 -10 10 20 - 20 -10 10 20 - 10 - 10 - 20 - 20아
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find u + v, u – v, and 3u – 4v. Then sketch each resultant vector.
= (0, -6), v = (1, –2)
u =
(a)
u + v
u + v =
y
2
y
21
X
-6
-4
-2
2
4
6.
-6
-4
-2
2
4
6.
-2
-4
-6
6
V
V
-8
u + v
-8
u + v
- 10
- 10
y
10
y
10
u + v
U+ V
V
V
5F
u
u
-6
-4
-2
2
4
-6
-4
-2
2
4
-5
(b)
u - v
u - v =
y
y
6
6
4
4
2
2
-6
-4
-2
2
4
6
-6
-4
-2
4
12
-2
u
u
u - v
-4
u - v
-4
-v
-v
-6
-6
-81
-81
y
81
y
8
6
6
-v
-v
4
4
U – v
u - v
2
- X
X
-6
-4
-2
4
6
-6
-4
-2
4
6
-2
-2
-4
-4
- 6
- 6
(c)
3u – 4v
3u – 4v =
y
y
20
20
10
10
X
- 20
- 10
10
- 20
- 10
10
20
3u
3 u
3u – 4v
\3 u – 4 v
-10
- 10
-4v
-4 v
– 20
- 20
y
20
20
-4v
-4v
10
10
3u - 4v
3u – 4v
3u
3u
- 20
- 10
10
20
- 20
- 10
10
20
- 10
- 10
- 20
- 20
20
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