Question

If `bara + barb = barc, |bara| = sqrt(5), |barb| = sqrt(2), |barc|` = 3, then the angle between `barb` and `barc` is ______.

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

If `bara + barb = barc, |bara| = sqrt(5), |barb| = sqrt(2), |barc|` = 3, then the angle between `barb` and `barc` is 45°.

Explanation:

`bara + barb = barc`

∴ `bara = barc - barb`

Squaring both sides

`|bara|^2 = |barc - barb|^2`

∴ `|bara|^2 = (barc - barb)*(barc - barb)`

∴ `|bara|^2 = |barc|^2 - 2barc*barb + |barb|^2`

∴ 5 = `9 - 2barc*barb + 2`

∴ `2barc*barb` = 6,

∴ `barc*barb` = 3

∴ `|barc|*|barb|cosθ` = 3,   ...(θ is the angle between `barc` and `barb`)

`3sqrt(2)cosθ` = 3

∴ cos θ = `1/sqrt(2)`

∴ θ = 45°