Question

Vectors v and w are given in magnitude and direction form. Find the coordinate representation of the sum v + w

and the difference v − w. Give coordinates to the nearest tenth of a unit.
a. v: magnitude 12, direction 50° east of north
w: magnitude 8, direction 30° north of east
b. v: magnitude 20, direction 54° south of east
w: magnitude 30, direction 18° west of south

Answer 1

a) v + w = 13.2 i + 14.6 j

v - w = 5.2 i + 0.8 j

b) v + w = 2.5 i - 44.7 i

v - w = 21 i + 12.4 i

Explanation:

a) For v: ∡ = 90º-50º = 40º

v = 12*cos 40º i + 12*Sin40º j

For w: ∡ = 90º-30º = 60º

w = 8*Cos 60º i + 8*Sin 60º j

v + w = (12*cos 40º+8*Cos 60º) i + (12*Sin40º+8*Sin 60º) j

v + w = 13.2 i + 14.6 j

v - w = (12*cos 40º-8*Cos 60º) i + (12*Sin40º-8*Sin 60º) j

v - w = 5.2 i + 0.8 j

b) For v: ∡ = -54º (clockwise)

v = 20*cos (-54º) i + 20*Sin(-54º) j

For w: ∡ = 270º-18º = 252º

w = 30*Cos 252º i + 30*Sin 252º j

v + w = (20*cos (-54º)+30*Cos 252º) i + (20*Sin(-54º)+30*Sin 252º) j

v + w = 2.5 i - 44.7 i

v - w = (20*cos (-54º)-30*Cos 252º) i + (20*Sin(-54º)-30*Sin 252º) j

v - w = 21 i + 12.4 i