Question

if the magnitude of dot and cross product is equel then the angle between two vectors in degree is​

Answer 1

Dot product is maximum when two non-zero vectors are perpendicular to each other. Two vectors are parallel ( i.e. if angle between two vectors is 0 or 180 ) to each other if and only if a x b = 1 as cross product is the sine of angle between two vectors a and b and sine ( 0 ) = 0 or sine (180) = 0.☺

Answer 2

Answer:

Let x and y be our two vectors whose dot product and cross product have the same magnitude. So we see know that ∥x×y∥=∥x⋅y∥ so ∥x×y∥∥x⋅y∥=1 . From vector analysis, we know that the dot product of two vectors can be written in terms of their intersecting angle θ as x⋅y=∥x∥∥y∥cosθ and the cross product can be written as ∥x×y∥=∥x∥∥y∥sinθ . We can divide the equations and see 1=∥x×y∥∥x⋅y∥=∥x∥∥y∥sinθ∥x∥∥y∥cosθ=tanθ. From here we can clearly see that tanθ=1 which implies when we restrict our answer to [0,π] thus θ=π4.