When the component of a vector A along the direction of vector B is zero, what can you conclude about the two vectors? Explain.

Question

When the component of a vector \(\vec A\) along the direction of vector \(\vec B\)  is zero, what can you conclude about the two vectors? Explain.

Answer 1

The two vectors A and B are perpendicular to each other.

Explanation – Let θ = angle between the two vectors A and B.

Therefore component of vector \(\vec A\) along the direction of vector \(\vec B\) is obtained resolving vector \(\vec A\) i.e. A cos θ

Now according to statement

A cos θ = 0

cos θ = 0 = cos 90º

∴ θ = 90º

i.e., \(\vec A\) ⊥ \(\vec B\)