Find the dot product of the given vectors.

u=2i-6j

v=3i+9j

u = 2i - 6j

v = 3i + 9j

Take the dot product:

u • v = (2i - 6j) • (3i + 9j)

u • v = (2i • 3i) + (2i • 9j) + (-6j • 3i) + (-6j • 9j)

u • v = 6 (i • i) + 18 (i • j) - 18 (j • i) - 54 (j • j)

The dot product is defined so that for the orthogonal unit vectors i and j, we have i • i = j • j = 1, and i • j = 0. So the above reduces to

u • v = 6 + 0 - 0 - 54

u • v = - 48