Question

If `hat a` and `hat b` are unit vectors that make an angle of 60 degrees with each other, calculate?

a) `|3hata-5hatb |`
b) `|8hata+3hatb |`

Answer 1

`sqrt(19)` and `sqrt(97)`

Explanation:

If two vectors `vec"A"` and `vec"B"` are making an angle `θ` then

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

Multiplying a vector with positive integer doesn’t change its direction. So,

• `3hata` and `5hatb` are at angle `60°`
• `8hata` and `3hatb` are also at an angle `60°`

a)
`|3hata - 5hatb| = sqrt(3^2 + 5^2 - (2 × 3 × 5 × cos60)) = sqrt(19)`

b)
`|8hata + 3hatb| = sqrt(8^2 + 3^2 + (2 × 8 × 3 × cos60)) = sqrt(97)`