How do you find the inner product and state whether the vectors are perpendicular given #<7,-2,4>*<3,8,1>#?

1 Answer
Jul 11, 2016

Answer:

Dot product = 9. Vectors are not orthogonal.

Explanation:

#vec(u)*vec(v) = sum_(i=1)^n u_iv_i " for " vec(u),vec(v) in RR^n#

So, in #RR^3# the dot product will be given by #sum_(i=1)^3u_iv_i#

#=7*3 + (-2)*8 + 4*1 = 9#

For orthogonality, think about the other definition of the dot product:

#vec(u)*vec(v) = |vec(u)||vec(v)|costheta#

If the vectors are orthogonal, #theta = pi/2# and the dot product is zero. This is how you can check orthogonality with the dot product. As you can see, the dot product of these two vectors is non-zero and thus they are not orthogonal.