00:01
We have two vectors where in vector u, we're missing a component, and they're calling it x, and these two vectors are supposed to have an angle between them of 30 degrees.
00:10
So we have this formula here.
00:13
So cosine of 30 is supposed to equal u dotted with v, so that's 7x minus 6.
00:24
It's x times 7 plus 2 times negative 3 over the magnitude of u.
00:29
So that's x squared plus two squared times the magnitude of v which is seven squared plus negative three squared.
00:44
So let's keep simplifying.
00:46
Cosine of 30 is 0 .866 and then we have 7x minus 6.
00:58
X squared plus 2 squared that's x squared plus 4 and the other one is 49 plus 9 so we have 0 .866 equals 7x minus 6 and then the 49 plus the 9 is 58 so that's 58 and x squared plus 4 it's just the two radicals bind into one radical.
01:32
Okay, so we can put a one, we can cross multiply, so we get 7x minus 6 equals 0 .866 times radical 58x squared, i'm distributing here, plus 232.
01:58
Okay, so this is literally a mess.
02:04
Square both sides to get rid of our square root.
02:09
Okay, and then we're going to have 7x minus 6 times 7x minus 6, and we're going to have to foil that...