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()


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