Question

How do you find the magnitude of `<5,6>` and write it as a sum of the unit vectors?

Answer 1

`"magnitude" = 7.810`

`< 5,6 > = 5hati + 6hatj`

Explanation:

We'll call the given vector `vecA` with components `A_x = 5` and `A_y = 6`.

The magnitude of a vector is given by

`|vecA| = sqrt((A_x)^2 + (A_y)^2) = sqrt(5^2 + 6^2) = color(blue)(ulbar(|stackrel(" ")(" "7.810" ")|)`

`" "`

Vectors in the notation `< x,y >` can also be represented by unit vectors, with the unit vector `hati` for the `x`-component and `hatj` for the `y`-component:

`< 5,6 > = color(blue)(ulbar(|stackrel(" ")(" "5hati + 6hatj" ")|)`