Question

If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is ______.

Options

• `π/2`

• `π/3`

• `π/4`

• `π/6`

Answer 1

If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is `underlinebb(π/3)`.

Explanation:

Given `bara + barb + barc = bar0`,

`|bara|` = 3, `|barb|` = 5, `|barc|` = 7

`\implies (bara + barb).(bara + barb) = (-barc).(-barc)`

`\implies` |a|² + |b|² + 2|a||b| cos θ = |c|²

`\implies` 9 + 25 + 30 cos θ = 49

`\implies` cos θ = `1/2`

∴ Angle between `bara` and `barb` is `π/3`