Question

Two vector have equal magnitude and their resultant also have the same magnitude, what is the angle between the two vectors? ​

Answer 1

Answer:

The angle between the two vectors is 60°

Explanation:

Let A and B represent the two vectors, we have;

$\left | A \right | = \left | B \right | = \left | A + B\right |= \left | R\right |$

Let $\left | A \right |$ = a, $\left | B\right |$ = b, and $\left | R\right |$ = c

We have by cosine rule

c² = a² + b² - 2 × a × b × cos(C)

Where, the angle "C", is the angle between the resultant of the two vectors, a and b and facing the resultant $\left | R\right |$

Given that, a = b = c, we have;

a² = a² + a² - 2 × a × a × cos(C)

a² = 2·a² - 2 × a² × cos(C)

2 × a² × cos(C) = 2·a² - a²

cos(C) = a²/(2·a²) = 1/2

Therefore, angle ∠C = arccosine(1/2) = 60°

The angle between the two vectors = ∠C = 60°.