How do you compute the dot product for #u=i-2j# and #v=-2i+j#?

1 Answer
Nov 10, 2016

Answer:

# :. ulu * ulv = -4 #

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 #

Inner Product = 0 #hArr# vectors are perpendicular

So, # ulu=ulhati-2ulhatj#, and #ulv=-2ulhati+ulhatj#

Then the inner product is given by;
# ulu * ulv = (1)(-2) + (-2)(1)#
# :. ulu * ulv = -2 - 2#
# :. ulu * ulv = -4 #