Question

Find component of vector A +B along (i) x-axis, (ii) C. Given `A = hati - 2hatj, B=2hatj+3hatk` and `C = hati +hatj`.

Answer 1

`A+B=(hati - 2hatj)+(2hati+3hatk) = 3hatj- 2hatj+3hatk`
(i) Component of A+B along x-axis is 3.
(ii) Component of A+B = R (say) along C is
`R cos theta =(R.C)/(C ) = R cos theta=(R.C)/(C)=((3hati-2hatj+3hatk).(hati+hatj))/(sqrt((1)^(2)+(1)^(2)))=(3-2)/(sqrt2)=(3)/(sqrt(14))`
`theta=cos^(-1)((3)/(sqrt(14)))`