Question

if the angle between two vectors wjpose magnitudes are in the ratio 3:4 is 30 degrees,then what is the angle made by the resultant vector with the first vector

Answer 1

Let the magnitudes of the vectors be, 3x and 4x. The angle between is 30o.

The resultant makes an angle θ with the first vector whose magnitude is 3x.

So, tanθ = (4x sin30)/(3x + 4x cos30) = 4/(6 + 4√3)

=> θ = tan-1(0.3094)

=> θ = 17.2o