How do I find the dot product of vectors #v =5i-2j# and #w=3i+4j#?

1 Answer
Dec 31, 2014

#vecv*vecw=7#
The dot product is a scalar obtained by multiplying the corresponding components of the two vectors and adding (algebraically) the results.
So you have:
#vecv*vecw=(5*3)+(-2*4)=15-8=7#

You may check your result by plotting your vectors and using the alternative definition of dot product:

#vecv*vecw=|vecv|*|vecw|*cos(theta)#
i.e.: the product of the modulus of the vectors times de cosine of the angle between them.
enter image source here
After some inverse trigonometry and Pitagora's Theorem I got:
#|vecv|=5.4#
#|vecw|=5#
#|theta_v|=21.8°#
#|theta_w|=53.1°#
and #theta=21.8°+53.1°=74.9°#
so that:
#vecv*vecw=5*5.4*cos(74.9°)=7#