Question

Find the direction ratios of a line perpendicular to both the lines whose direction ratios are 3, –2, 1 and 2, 4, –2

Answer 1

The vectors along the given lines are:

`bara = 3hati - 2hatj + hatk` and `barb = 2hati + 4hatj - 2hatk`

The vector perpendicular to both the vectors is given by `bara xx barb`

∴ `bara xx barb = |(hati, hatj, hatk),(3, -2, 1),(2, 4, -2)|`

= `hati(4 - 4) - hatj(-6 - 2) + hatk(12 + 4)`

= `0hati + 8hatj + 16hatk`

∴ The direction ratios of required line are 0, 8, 16 i.e. 0, 1, 2