Question

The angle between two lines `(x + 1)/2 = (y + 3)/2 = (z - 4)/(-1)` and `(x - 4)/1 = (y + 4)/2 = (z + 1)/2` is ______.

Options

• `cos^-1(2/9)`

• `cos^-1(4/9)`

• `cos^-1(5/9)`

• `cos^-1(7/9)`

Answer 1

The angle between two lines `(x + 1)/2 = (y + 3)/2 = (z - 4)/(-1)` and `(x - 4)/1 = (y + 4)/2 = (z + 1)/2` is `underlinebb(cos^-1(4/9))`.

Explanation:

cosθ = `|a_1a_2 + b_1b_2 + c_1c_2|/(sqrt(a_1^2 + b_1^2 + c_1^2)sqrt(a_2^2 + b_2^2 + c_2^2))`

cosθ = `|2 + 4 - 2|/(3 xx 3) = 4/9`