Question

Find the angle between the lines `barr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk)` and `barr=5 hati-2hatk+mu(3hati+2hatj+6hatk)`

Answer 1

Let  `barb_1` and  `barb_2` be the vectors in the direction of the lines 

Let θ be the acute angle between the two given lines.

`therefore cos theta=(barb_1barb_2)/(|barb_1||barb_2|)=19/(3xx7)`

`therefore cos theta =19/21`

`theta=cos^-1(19/21)`