Question

Compute the resultant of three coplanar vectors P, 2P and 3P inclined at 120° with one another.​

Answer 1

Answer:

Theta = 210 degree

Explanation:

Rx= pcos0° + 2pcos120°+3pcos240°

= p+2p(-1/2)+3p(-1/2)

=p-p-3p/2= -3p/2

Ry=psin0°+2psin120°+3psin240°

=0+2p(√3/2)+3p(-√3/2)

=(2-3)√3/2p= -√3/2p

Resultant,R= (√Rx square + √ Ry square)

= √3p

tan theta = Ry/Rx

= -√3/2p/-3/2p = 1/√3= tan30° or tan210°

As Rx and Ry are both negative, R must be in the third quadrant and theta = 210°