Write a vector of magnitude 12 units which makes 45° angle with X-axis, 60° angle with y-axis and an obtuse angle with Z-axis.

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

Given that α=45°, β=60° and m= 12. We have to figure out the vector.

Since cos²α+cos²β+cos²γ=1, we get

cos²45°+cos²60°+cos²γ=1

Since γ is obtuse, .

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

So the required vector is

Rationalizing, we get