Question

What is the angle between the vectors `hati - 2hatj + 3hatk` and `3hati - 2hatj + hatk`

Options

• `cos^-1 (5)`

• `cos^-1 (7)`

• `cos^-1  5/7`

• `cos^-1  7/5`

Answer 1

`cos^-1  5/7`

Explanation:

Let `veca = hati - 2hatj + 3hatk` and `vecb = 3hati - 2hatj + hatk` are the given vectors and let θ be the angle between them than,

cos θ = `(veca * vecb)/(|veca||vecb|)`  ......(1)

Now, `veca * vecb = (hati - 2hatj + 3hatk) * (3hati - 2hatj + hatk)`

= `(1) (3) + (-2) (-2) + (3) (1)`

= 3 + 4 + 3 = 10

`|veca| = sqrt((1)^2 + (-2)^2 + (1)^2`

= `sqrt(9 + 4 + 1)`

= `sqrt(14)`

From (1) we get,

`cos theta = (veca * vecb)/(|veca||vecb|)`

= `10/(sqrt(14) sqrt(14))`

= `10/14`

= `5/4`

∴ θ =  `cos^-1 (5/7)`