Vector Quantities

Question

If vector v = 2i + 3j,

How do I solve v times v?

Answer 1

What you're likely thinking of is vector dot product. You add the product of each component to itself. e.g.

v*v = (2*2) + (3*3)

The result is a scalar value.

Answer 2

In two dimensions, the typical product of two vectors that one defines is the dot product.

If v = ai + bj and w = ci+dj, then the dot product of v and w is defined by

v•w = ac + bd. Note that this product is a number rather than another vector.

In your example with v = 2i+ 3j, we have

v•v = (2i+3j)•(2i+3j) = 2(2) + 3(3) = 13.