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

1 Answer
Nov 1, 2016

Answer:

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