Find a vector a of magnitude 5√2 making an angle of π/4 with x-axis, π/2 with y-axis and an acute angle θ with z-axis.

Given, vector |V| = 5√2 ⇒ a² + b² + c² = 50
The direction of cosines of A are
Angle with x - axis
cos α = x/|A| = x/5√2
cos α = π/4 = 1/√2
So, 1/√2 = x/5√2
x = 5
Angle with y - axis
Similarly for
cos α = y/|A| = y/5√2
cos α = π/2 = 0
So, 0 = y/5√2
y = 0
a² + b² + c² = 50
25 + 0 + c² = 50
c² = 25
c = ±5
Angle with z-axis is acute. cos θ > 0 so c = 5
Therefore, the vector V = 5î + 0ĵ + 5k̂.