The magnitudes and directions of three vector are shown the

The magnitudes and directions of three vector are shown the figure. The magnitude and direction of the resultant of these vectors are:

a) 22m & 555o

b) 6.731m & 512.144o

c) 8.375 m & 312.144o

d) 8.3.75 m & 47.856o

Solution

1st vector : 7 angle 45 deg

2nd vector : 10 angle 300 deg

3rd vector : 5 angle 210 deg

Resultant : X component = 7cos45 + 10 cos(360 -300) - 5cos30

= 5.619 units

Y component = 7sin45 - 10sin60 - 5sin30 = - 6.21 units

Resultant = sqrt(5.619^2 + 6.21^2) = 8.37

Angle = 2pi - tan^-1(6.21/5.619) = 312.14 deg

Option C