Given the vectors #u=<2,2>#, #v=<-3,4>#, and #w=<1,-2>#, how do you find #(v*u)-(w*v)#?

1 Answer
Nov 1, 2016

Answer:

# (vec v * vec u) - (vec w * vec v) = 13 #

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 #
=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+

So with, # vecu=<<2,2>>#, and # vecv=<<-3,4>> #, and # vecw=<<1,-2>> # we get:

# (vec v * vec u) - (vec w * vec v) = { (-3)(2) + (4)(2) } - { (1)(-3) + (-2)(4) } #
# :. (vec v * vec u) - (vec w * vec v) = {-6 + 8 } - {-3 -8 } #
# :. (vec v * vec u) - (vec w * vec v) = 2 - {-11 } #
# :. (vec v * vec u) - (vec w * vec v) = 13 #