The resultant of three vectors 1,2, and 3 units whose directions are those of the sides of an equilateral triangle is at what angle with respect to first vector?

Options

A. `30^(@)` with the first vector
B. `15^(@)` with the first vector
C. `100^(@)` with the first vector
D. `15^(@)` witht the first vector

Answer

a

Explanation

Take the vector 1 along x -axis resolving the vector `R_(x) = 1 + 2 cos 120^(@) - 3 cos 240^(@), R_(y) 2 sin 120^(@) + 3 sin 240^(@), R_(x) = -3//2`,
`R_(y) = sqrt(3)//2, tan theta = R_(y)//R_(x) = (1)/(sqrt(3)), theta = 30^(@)`