Question

For which angle between two equal vectors `vec"A"` and `vec"B"` will the magnitude of the sum of two vectors be equal to the magnitude of each vector?

Options

• θ = 60°

• θ = 120°

• θ = 0°

• θ = 90°

Answer 1

θ = 120°

Explanation:

`|vec"A"+vec"B"|=sqrt("A"^2+"B"^2+2"AB"cos120°)`  (θ = 120°)

= `sqrt("A"^2+"B"^2+2"AB"((-1)/2)) (cos120° = -1/2)`

= `sqrt("A"^2+"B"^2-"A"("A"))`

= `sqrt("B"^2)` = B   (∴ A = B)