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

1 Answer
Feb 8, 2017

Answer:

#(3w * v)vec(u) = <<-66,-66>>#

Explanation:

Inner Product Definition
If # ulu = <<(u_1, u_2)>> #, and # ulv = <<(v_1, v_2)>> #, then the inner product (or dot product), a scaler quantity, is given by:

# ulu * ulv = u_1v_1 + u_2v_2 #

So, # vec(u)=<<2,2>>#, #vec(v)=<<-3,4>>#, and #vec(w)=<<1,-2>>#

Then the inner product #(3w * v)# is given by;

# 3vec(w) * vec(v) = 3<<1,-2>> * <<-3,4>> #
# " "= <<3,-6>> * <<-3,4>> #
# " "= (3)(-3) + (-6)(4) #
# " "= -9 -24 #
# " "= -33 #

And so the vector #(3w * v)vec(u)# is:

#(3w * v)vec(u) = -17vec(u)#
#" "= -33<<2,2>>#
#" "= <<-66,-66>>#