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

1 Answer
Nov 2, 2016

Answer:

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