Question

when a vector cross b vector is equal to a vector dot b vector.​

Answer 1

Answer :-

♦ We must know what is

$\vec{a}$ • $\vec{b}$

= magnitude of a × magnitude of b × cos of angle between them .

= $ab \:cos\theta$

$\vec{a} \times \vec{b}$

= magnitude of a × magnitude of b × sin of angle between them

= $ab \: sin\theta$

♦ Now to get the same result from both (•) dot and (×) product .

sin∅ should be = cos∅

Or

∅ = 45°

As

$sin45^{\circ} = \dfrac{1}{\sqrt{2}} = cos 45^{\circ}$