Question

The direction cosines of a line which is perpendicular to lines whose direction ratios are 3, - 2, 4 and 1, 3, - 2 are ______.

पर्याय

• `4/sqrt297, 5/sqrt297, 16/sqrt297`

• `8/sqrt285, 10/sqrt285, 11/sqrt285`

• `(-8)/sqrt285, (10)/sqrt285, (11)/sqrt285`

• `(-8)/sqrt285, (-10)/sqrt285, (11)/sqrt285`

Answer 1

The direction cosines of a line which is perpendicular to lines whose direction ratios are 3, - 2, 4 and 1, 3, - 2 are `underline((-8)/sqrt285, (10)/sqrt285, (11)/sqrt285)`.

Explanation:

Given direction ratio

(3, - 2, 4) and (1, 3, - 2)

Direction ratio of line which is perpendicular to both vector is

`(3hat"i" - 2hat"j" + 4hat"k") xx (hat"i" + 3hat"j" - 2hat"k")`

i.e., `|(hat"i", hat"j", hat"k"),(3,-2,4),(1,3,-2)| = - 8hat"i" + 10hat"j" + 11hat"k"`

i.e., (- 8, 10, 11)

Direction cosine is

`(- 8)/(sqrt(8^2 + 10^2 + 11^2)), 10/(sqrt(8^2 + 10^2 + 11^2))`,

`11/(sqrt(8^2 + 10^2 + 11^2)), ((- 8)/sqrt 285, 10/sqrt 285, 11/sqrt 285)`