Question

What is the dot product of `<3,-7,6 >` and `<4,1,7 >`?

Answer 1

The dot product of two vectors, also called the 'scalar product' is a single number, in this case `47`.

Explanation:

To find the dot product (scalar product) of two vectors `[a_1, a_2, a_3, ..., a_n]` and `[b_1, b_2, b_3, ..., b_n]`, we simply multiply the corresponding elements and add all the products:

`a_1b_1 + a_2b_2 + a_3b_3 + .... + a_nb_n`

In this case, the dot product is:

`3*4+(-7)*1+6*7 = 12 - 7 + 42 = 47`