If a line makes angles 90°, 135°, 45° with x, y and z axes respectively, find its direction cosines.

Or

Find the vector equation of the line which passes through the point (3,4,5) and is parallel to the vector .

Direction cosines of a line making angle α with x-axis, β with y-axis and γ with z-axis are l, m ,n.

l = cos α , m = cos β , n = cos γ

Here, α = 90° , β = 135° and γ = 45°

l = cos 90°

=0

m = cos 135°

= cos(180° - 45°)

n = cos 45°

OR

If the coordinates of a point A= (x₁, y₁, z₁), then the position vector is

Hence, the position vector of point P = (3,4,5) is

If the position vector () of a point on the line and a vector () parallel to the line is given, then the vector equation of a line is given by

Here, and , then