00:01
Okay, so let's call this vector here a, let's call this vector here b, and this guy angle c.
00:06
So a dot b is equal to a magnitude, b magnitude, cosine theta.
00:14
Okay, so we need to plug this stuff in.
00:18
So let's do a.
00:20
.b is going to be 2 plus x.
00:25
Magnitude of a is going to be square root of two squared plus one squared plus negative one squared so this is going to be rad six and that's magnitude of b is going to be uh it ends up being one plus x squared okay square root of that okay so plugging all this into this formula we get two plus x is equal to rad six plus this and then cosine of 45 is 2 rad 2.
01:00
Okay, so what we're going to do is we're going to square both sides of this equation.
01:06
Squaring both sides, we get 4 plus 4x plus x squared plus 6x, and then if we square this, we get 1⁄2.
01:21
Okay, so then let's just rewrite that 4 plus 4x plus x squared is equal to 1 half of 6 plus 6 .6 x squared.
01:31
This is a quadratic equation.
01:33
So we've got 4 plus 4x plus x squared is equal to 3 plus 3x squared...