Question

The angle between vectors A + B and vectors A×B is
​

Answer 1

We have been supplied with two vectors : A and B.

To find :

angle between (A + B) and (A × B)

Concept:

Let's consider 2 vectors :

• $\vec A\: and\: \vec B$

We know that vector additionbetween two factors result in another vector line in the same plane as that of the 2 parent vectors.

$\vec A + \vec B = \vec C$

So $\vec C$ will lie in the same plane as $\vec A \:and \:\vec B$.

Now coming to Cross product of vectors :

Cross product factors lead to formation of another vector which is perpendicular to the plane of the 2 previous factors.

$\vec A \times \vec B = \vec D$

So , $\vec D$ will be present perpendicular to the plane of $\vec A \:and \:\vec B$.

So angle between $\vec C\: and\: \vec D$ will be 90°.

So final answer is 90°.