Find a vector of magnitude making an angle π/4 with x - axis, π/2 with y - axis and an acute angle θ with z - axis.
|| = 5√2
l = cos α = cos π/4 = 1/√2
m = cos β = cos π/2 = 0
n = cosθ
we know that
l2 + m2 + n2 = 1
since the vector makes an acute angle with the z axis
∴
∴ = ||(l + m + n)
∴ = 5√2(1/√2 + 1/√2)
∴ = 5()
Ans: = 5()