Question

Question #d7dc2

Answer 1

We know with reference to the given figure that by Law of parallelogram of vectors

`|vecR|=sqrt(|vecP|^2+|vecQ|^2+2|vecP|cdot|vecQ|cdot cos theta)` .....(1)
and `alpha=tan^-1((|vecQ|sin theta)/(|vecP|+|vecQ|cos theta))` .....(2)

Inserting given values in equation (1) we get

`|vecR|=sqrt(|5|^2+|-3|^2+2|5|cdot|-3|cdot cos 60)`
`=>|vecR|=sqrt(23+9+2xx5xx3xx 0.5)`
`=>|vecR|=sqrt47`
`=>|vecR|=6.86`, rounded to two decimal places