Question

The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.

पर्याय

• `sqrt(35)`

• `sqrt(37)`

• `sqrt(38)`

• `sqrt(39)`

Answer 1

The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is `underlinebb(sqrt(35))`.

Explanation:

Let P = (2, – 3, 1),

A = (–1, 3, –1)

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

`|bar(AP)| = sqrt(9 + 36 + 4)` = 7

Vector along the given line is `barb = 2hati + 3hatj - hatk`

AM = Projection of `bar(AP)` on `barb`

= `|(bar(AP)*barb)/|barb||`

= `|(6 - 18 - 2)/sqrt(14)|`

= `sqrt(14)`

By Pythagoras theorem:

PM = `sqrt(49 - 14)`

= `sqrt(35)`