Question

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

Answer 1

The angle between the two vectors is 60°

Step-by-step 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°.