Question

How do you find the inner product and state whether the vectors are perpendicular given `<3,1,4>*<2,8,-2>`?

Answer 1

The inner product is `6`
The vectors are not perpendicular.

Explanation:

Inner Product Definition
If `vecu = <<(u_1, u_2, u_3)>>`, and `vecv = <<(v_1, v_2, v_3)>>`, then the inner product (or dot product), a scaler quantity, is given by:
`vecu * vecv = u_1v_1 + u_2v_2 + u_3v_3`

Inner Product = 0 `hArr` vectors are perpendicular

So,
Let `vecA=<<3,1,4>>`, and `vecB=<<2,8,-2>>`

Then the inner product is given by;
`vecA * vecB = (3)(2) + (1)(8) + (4)(-2)`
`vecA * vecB = 6 + 8 -8 = 6`

`vecA * vecB != 0 rArr` vectors are not perpendicular