Question

Direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are ______.

Options

• 1, 1, 2

• 2, –1, 2

• –2, 1, 2

• 2, 1, –2

Answer 1

Direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are 2, –1, 2.

Explanation:

Let the direction ratios of a line are (a, b, c).

As, line is perpendicular to the direction ratios (–1, 2, 2) and (0, 2, 1).

∴ a × –1 + b × 2 + c × 2 = 0 and a × 0 + b × 2 + c × 1 = 0

`\implies` – a + 2b + 2c = 0 and 0a + 2b + c = 0

`\implies` `a/(2 - 4) = (-b)/(-1 - 0) = c/(-2 - 0)`

 `\implies` `a/-2 = b/1 = c/-2` or `a/2 = b/-1 = c/2`

Hence, the direction ratios of a line are (2, –1, 2).