Question

find the angle between two vectors if their vector product is equal to scalar product

Answer 1

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$let \: the \: vector \: be \: \frac{}{a} and \: \frac{}{b} \\ now \: cross \: product \\ \frac{}{a} \times \frac{}{b} = | \frac{}{a} | \times | \frac{}{b} | \sin( \alpha ) \\ given \: that \: cross \: product \: is \: equal \: to \: scalar \: product \\ so \\ | \frac{}{a} | \times | \frac{}{b} | = | \frac{}{a} | \times | \frac{}{b} | \: \sin( \alpha ) \\ \sin( \alpha ) = 1 \\ \alpha = \frac{\pi}{2}$
Hope it will help you✔️

Answer 2

The angle between two vectors, deferred by a single point, called the shortest angle at which you have to turn around one of the vectors to the position of co-directional with another vector.

Explanation:

Basic relation. The cosine of the angle between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.

                 

cos α =  a·b/|a|·|b|