Question

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

Answer 1

`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.

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`