Question

How do you find the inner product and state whether the vectors are perpendicular given `<3,5>*<4,-2>`?

Answer 1

The inner product is `2`
The vectors are not perpendicular.

Explanation:

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

Inner Product = 0 `hArr` vectors are perpendicular

So,
Let `vecA=<<3,5>>`, and `vecB=<<4,-2>>`

Then the inner product is given by;
`vecA * vecB = (3)(4) + (5)(-2)`
`vecA * vecB = 12 - 10 = 2`

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