Question #ea7e8
1 Answer
We have vectors
# (bb(ul a) * bb(ul b))^2 = | bb(ul a) |^2 \ | bb(ul b) |^2 #
Using the definition of the dot (or scalar) product, and denoting the angle between
# (| bb(ul a) | \ | bb(ul b) | \ cos theta)^2 = | bb(ul a) |^2 \ |bb(ul b)|^2 #
And so:
# | bb(ul a) |^2 \ |bb(ul b)|^2 - | bb(ul a) |^2 \ | bb(ul b) |^2 \ cos^2theta = 0#
# :. | bb(ul a) |^2 \ |bb(ul b) |^2 \ ( 1 - cos theta )= 0#
Leading to:
A) Either:
# => bb(ul a) = 0# or# bb(ul b) = 0#
But we are given that
B) Or:
# => theta =0 #
# => bb(ul a)# and# bb(ul b) # are parallel QED.