The magnitudes and directions of three vector are shown the

The magnitudes and directions of three vector are shown the figure.

Solution

let a=7cos45^o i + 7sin 45^o j

b=10cos300^o i + 10sin300^o j

c=5cos210^o i +5sin210^o j

resultant vector ia r=a+b+c

r=(7cos45^o i + 7sin 45^o j) +(10cos300^o i + 10sin300^o j) +(5cos210^o i +5sin210^o j)

r=(7cos45^o+10cos300^o +5cos210^o)i + (7sin 45^o+ 10sin300^o +5sin210^o )j

r=((7/2) +5 -(53 /2) )i + ((7/2) - (53 /2) -(5/2) )j

r=(5.6196)i + (-6.2105)j

magnitude =[(5.6196)² + (-6.2105)²]=8.375

direction angle =360- tan^-1(6.2105/5.6196)= 312^o