Question

lf `overlinea` and `overlineb` be two unit vectors and θ is the angle between them, then `|overlinea - overlineb|` is equal to ______

Options

• sin`(theta/2)`

• 2sin`(theta/2)`

• cos`(theta/2)`

• 2cos`(theta/2)`

Answer 1

lf `overlinea` and `overlineb` be two unit vectors and θ is the angle between them, then `|overlinea - overlineb|` is equal to `underline(2sin(theta/2))`.

Explanation:

`|overlinea - overlineb|^2 = (overlinea - overlineb).(overlinea - overlineb)`

= `overlinea.overlinea - overlinea.overlineb -  b.overlinea + overlineb.overlineb`

= 1 - 2 `overlinea.overlineb + 1` ............`[∵ |overlinea| = |overlineb| = 1]`

= 2 - 2.1.1cos θ = 2(1 - cos θ)

= 2(2sin²`theta/2`) 

= 4 sin²`theta/2` 

∴ `|overlinea - overlineb| = 2 sin (theta/2)`