Let the angles made by vector be α, β, θ and the magnitude be m.
Given that \(\alpha=\cfrac{\pi}4,\) \(\beta = \cfrac{\pi}2\) and m = 5√2. We have to figure out the vector.
Since cos2α + cos2β + cos2θ = 1, we get
Since θ is acute, \(cos\theta=\cfrac{1}{\sqrt2}\)
Any vector, if it’s magnitude and direction cosines are given can be written as
So, the required vector is