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

Let the angles made by vector be α, β, θ and the magnitude be m.

Given that . We have to figure out the vector.

Since cos²α+cos²β+cos²θ=1, we get

Since θ is acute, .

Any vector, if it’s magnitude and direction cosines are given can be written as

So, the required vector is