Question

What is the dot product of `<5,1,-7>` and `<8,4,9>`?

Answer 1

The dot product of two three dimensional vectors is defined as

`a*b=a_x*b_x+a_y*b_y+a_z*b_z`

In our case `a=(5,1,-7)` and `b=(8,4,9)`

hence

`a*b=5*8+1*4-7*9=-19`

Answer 2

`-19`

Explanation:

To do the dot product, you multiply together the corresponding components, and then sum the results. In general:
`(a_1, a_2, a_3)*(b_1, b_2, b_3)=(a_1b_1+a_2b_2+a_3b_3)`

So in your case:

`(5*8)+(1*4)+(-7*9)`
`=40+4-63`
`=-19`