Question

The resultant of three vectors 1,2, and 3 units whose directions are those of the sides of an equilateral triangle is at an angle of
A. `30^(@)` with the first vector
B. `15^(@)` with the first vector
C. `100^(@)` with the first vector
D. `150^(@)` with the first vector

Answer 1

Correct Answer - D
Analytically:
`R_(x)=1+2 cos 120^(@)+3 cos 240^(@)=-3//2`
`R_(y)=2 sin 120^(@)+3 sin 240^(@)`
`=2xxsqrt(3)/2+3xx(-sqrt(3)/2)= - sqrt(3)/2`
`tan theta= R_(y)/R_(x)=(-sqrt(3)/2)/(-3/2) =sqrt(3)/3=1/sqrt(3)rArr theta=30^(@)`
Hence, angle with first vector is `180-theta=150^(@)`.

Graphically:
`AB=1, BC=2, CD=3`
`vec(R)=vec(AD)` is resultant, clearly angle between `vec(R )` and `vec(AB)` is `150^(@)`