Question

The direction ratios of a line perpendicular to the lines with direction ratios 1, 3, 2, and -1, 1, 2 are ______ 

विकल्प

• 1, 1, 2

• -1, 3, 2

• 4, -4, 4

• -4, 3, 2

Answer 1

The direction ratios of a line perpendicular to the lines with direction ratios 1, 3, 2, and -1, 1, 2 are 4, -4, 4.

Explanation:

Vectors having the given d.r.s. are,

`overlinea = hati + 3hatj + 2hatk` and `overlineb = -hati + hatj + 2hatk`

A vector perpendicular to both `overlinea` and `overlineb` is given by,

`overlinea xx overlineb = |(hati, hatj, hatk), (1, 3, 2), (-1, 1, 2)|`

= `(6 - 2)hati - (2 + 2)hatj + (1 + 3)hatk`

= `4hati - 4hatj + 4hatk`