Question

If the sum of two-unit vectors is a unit vector, then the magnitude of their difference is

Options

• `sqrt(2)` units

• `sqrt(5)` units

• `sqrt(3)` units

• 0 units

Answer 1

`sqrt(3)` units

Explanation:

Let two-unit vector `veca` and `vecb`.

Where `|veca| = 1, |vecb|` = 1

and `|veca + vecb|` = 1

⇒ ΔABC is an equilateral Δ

Here ∠BCD = 120° or `(2pi)/3`

Now `(veca - vecb)^2 = (veca - vecb)*(veca - vecb)`

= `|veca| + |vecb|^2 -2veca.vecb`.

= `1 + 1 - 2.|veca||vecb| cos theta`

= `1 + 1 - 2.1.1. ((-1)/2)` = 3

`veca - vecb = sqrt(3)`