00:02
We're given that u is equal to this vector 2 square root 3 2, and v is equal to the vector negative 1 square root 3.
00:20
And now we're asked to figure out the dot product of these two, u dotted with v.
00:27
So we just need to remember how to calculate the dot product.
00:31
We're going to take the first components, multiply them together, then take the second components, add them together, multiply them together, and then add those things together.
00:42
So just in case i wasn't clear, it looks like this.
00:54
And now we'll simplify.
01:04
So this just gives us zero.
01:09
Now we're also asked to figure out what the absolute value of u is and what the absolute value or length of v is.
01:18
So let's figure out the lengths or absolute values.
01:21
So here we need to remember a formula.
01:24
We're taking the square root of the sum of the squares of the components.
01:32
So that's what the length of u is.
01:36
Let's see.
01:37
What does that work out to be? 12 plus 4 is 4...