Question

Given vectors: A = (7, 60), B = (6.7, 130), C = (14, ­160), D = (3.5, 160)

Find:

1. R1 = A1.5B + 0.5C ­- 2D

2. R2= ­A + 1.5B ­ .5C + 2D

Part B

Find E such that

A + 1.5B + C + D + 2E = 0  Use the graphical method to find E

Answer 1

1)

R1 =  A1.5B + 0.5C ­- 2D

R1x = 7 * cos 60 * 1.5 * 6.7 * cos 130 + 0.5 * 14 * cos 160 - 2 * 3.5 * cos 160

R1x = - 22.61

and

R1y = 7 * sin 60 * 1.5 * 6.7 * sin 130 + 0.5 * 14 * sin 160 - 2 * 3.5 * sin 160

R1y = 46.67

so,

R1 = sqrt ( R1x² + R1y²)

R1 = 51.86

_____________________________

2. R2= ­A + 1.5B ­ .5C + 2D

R2x = 7 * cos 60 +  1.5 * 6.7 * cos 130 * 0.5 * 14 * cos 160 + 2 * 3.5 * cos 160

R2x = 39.415

and

R2y = 17.92

so,

R2 = sqrt ( R2x² + R2y²)

R2 = 43.3

___________________________

A + 1.5B + C + D + 2E = 0

7 * cos 60 +  1.5 * 6.7 * cos 130 +  14 * cos 160 + 3.5 * cos 160 + 2 * Ex = 0

Ex = 9.7

and

7 * sin 60 +  1.5 * 6.7 * sin 130 +  14 * sin 160 + 3.5 * sin 160 + 2 * Ey = 0

Ey = 9.873