Find the angle at which vectors i - j + k are inclined to each of co-o

1.	Find the angle at which vectors i - j + k are inclined to each of co-ordinate axes.
Answer» Let vector a = i - j + k then vector \|a\| = √(1₂+ (-1)²+ 1²) = √3 The unit vector in the direction of vector a is given by a = vector(a/\|a\|) = (1 - j + k)/√3 = (1/√3)i - (1/√3)j + (1/√3)k ∴ l = cos α = 1/√3, m = cos β = -1/√3, n = cos γ = 1/√3 α = cos^-1(1/√3), β = cos^-1(-1/√3), γ = cos^-1(1/√3)

Find the angle at which vectors i - j + k are inclined to each of co-ordinate axes.

Answer»

Let vector a = i - j + k then

vector |a| = √(1₂+ (-1)²+ 1²) = √3

The unit vector in the direction of vector a is given by

a = vector(a/|a|) = (1 - j + k)/√3 = (1/√3)i - (1/√3)j + (1/√3)k

∴ l = cos α = 1/√3, m = cos β = -1/√3, n = cos γ = 1/√3

α = cos^-1(1/√3), β = cos^-1(-1/√3), γ = cos^-1(1/√3)