Question

Find the sum of the vectors u and v it theta is the angle between them?

`u=12, v=21, theta=70`, the answer is 27.5, 24 degrees to `v`

Answer 1

If `P =` Magnitude of `vecP, Q =` Magnitude of `vecQ and θ =` Angle between two vectors then `R =` Magnitude of Resultant `vecR` and `α =` is direction of Resultant then

`R=sqrt(P^2+Q^2+2PQcostheta)`
`alpha=tan^-1((Qsin theta)/(P+Qcostheta))`, measured from `vecP`

Taking `P` as `v` and `Q` as `u`, we get

`R=sqrt(21^2+12^2+2xx21xx12xxcos70^@)`
`=>R=27.5\ units`

`alpha=tan^-1((12\ sin 70^@)/(21+12\ cos70^@))`
`=>alpha=24.2^@`