Question

The angle between lines `(x - 2)/2 = (y - 3)/(- 2) = (z - 5)/1` and `(x - 2)/1 = (y - 3)/2 = (z - 5)/2` is ______.

Options

• 30°

• 60°

• 45°

• 90°

Answer 1

The angle between lines `(x - 2)/2 = (y - 3)/(- 2) = (z - 5)/1` and `(x - 2)/1 = (y - 3)/2 = (z - 5)/2` is 90°.

Explanation:

Angle between lines `(x - x_1)/"a"_1 = ("y" - "y"_1)/"b"_1 = ("z" - "z"_1)/"c"_1` and `(x - x_2)/"a"_2 = ("y" - "y"_2)/"b"_2 = ("z" - "z"_2)/"c"_2` is given by `cos theta = (|"a"_1"a"_2 + "b"_1"b"_2 + "c"_1"c"_2|)/(sqrt("a"_1^2 + "b"_1^2 + "c"_1^2) sqrt("a"_2^2 + "b"_2^2 + "c"_2^2))`

Here, a₁ = 2, b₁ = - 2, c₁ = 1

and a₂ = 1, b₂ = 2, c₂ = 2

∴ cos θ = `(|2 xx 1 + (- 2) xx 2 + 1 xx 2|)/(sqrt((2)^2 + (- 2)^2 + (1)^2) sqrt((1)^2 + (2)^2 + (2)^2))`

`=> cos theta = (|2 - 4 + 2|)/(sqrt9 sqrt9)` = 0

`=> theta = pi/2`