Question # Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between

# Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between

them if the magnitude of the resultant is

(a) 1 unit

(b) 5 unit and

(c) 7 unit

Solution

Let ( |vec{A}|=3 quad|quad| vec{B} mid=4 )

( therefore quad|vec{R}|=sqrt{A^{2}+B^{2}}+2 A B cos theta )

( (vec{R})=sqrt{(3)^{2}+(4)^{2}+2(3)(4) cos theta} )

( |vec{R}|=sqrt{9+16+24 cos theta} )

( |vec{R}|=sqrt{25+24 cos theta} )

for ( R=1, cos theta=-1 ) or ( theta=180^{circ} )

For ( R=5, cos theta=0.08 theta=90^{circ} )

for ( R=7,cos theta=1 ) or ( theta=0^{circ} )