Two vectors of magnitude 9 and 7 inclined to each other at 60°. What is the magnitude of the resultant? At what angle is the resultant inclined to the vector of magnitude 9?

 Two vectors of magnitude 9 and 7 inclined to each other at 60°. What is the magnitude of the resultant? At what angle is the resultant inclined to the vector of magnitude 9?

Solution

Please ignore the misprint of 60° as 62°.

In the above question let the vector a be of magnitude 9 , and the vector b be of magnitude 7 with 60° the angle between them

Let the resultant be represented by c and it makes angle α with vector a.

|a|=9

|b|=7

Angle between them θ=60°

|c|=√{|a|²+|b|²+2|a||b|cos(θ)}

|c|=√{81+49+ 2×9×7×0.5}

|c|=√193 ~13.89

To find the angle made by the resultant with a

tan(α)= |b|sinθ/(|a|+|b|cosθ)

tan(α)= 7×(√3/2)/(9+7×0.5)

tan(α)=7√3/25

Therefore the resultant has magnitude of √193 and makes an angle α with the vector of magnitude 9 such that tan(α)=7√3/25