If |vector A x vector B| = vector A.vector B, what is the angle between vector A and vector B?

Question:

If {eq}\rm \left | \vec A \times \vec B \right | = \vec A \cdot \vec B, {/eq} what is the angle between {eq}\rm \vec A {/eq} and {eq}\rm \vec B \ {/eq}?

Vector and Scalar Products:

The cross product of two vectors is known a the vector product while the dot product is known as the scalar product.

{eq}\text{Cross Product}\\ \vec A \times \vec B = |A||B| \sin \theta\\ \text{Dot Product}\\ \vec A . \vec B = |A||B| \cos \theta\\ {/eq}where |A|,|B| are the magnitudes of A and B vectors while {eq}\theta {/eq} is the angle between them.

Answer and Explanation:

Given

{eq}\rm \left | \vec A \times \vec B \right | = \vec A \cdot \vec B,\\ \text{Using the rule of cross and dot products of vectors we...

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Vectors: Definition, Types & Examples

from Common Entrance Test (CET): Study Guide & Syllabus

Chapter 57 / Lesson 3
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