Question

What is the dot product of 5i and 8j?

Answer 1

`0`

Explanation:

A property of the scaler (or dot) product is that it is zero if the vectors are perpendicular which `5ulhati` and `8ulhatj` clearly are, so without any calculation we know the answer is zero.

We can show this if required:

Let `vec u=5 ulhati+0 ulhatj=((5),(0))`
and `vec v=0 ulhati+8 ulhatj=((0),(8))`

The scaler product is:

`vec u * vec v = ((5),(0)) * ((0),(8))`
`\ \ \ \ \ \ \ \ \ \ = (5)(0) + (0)(8)`
`\ \ \ \ \ \ \ \ \ \ = 0+0`
`\ \ \ \ \ \ \ \ \ \ = 0`