00:00Hi guys, so in this
00:02lesson we are going to
00:03find the angle between two
00:05lines. Now I wasn't sure
00:06if this even needed a
00:07full video because once I
00:09tell you this one thing
00:10you're good to go. The
00:12angle between the two lines
00:13are the angle between two
00:15lines is the same as
00:16the angle between their direction
00:18vectors. Now that makes sense
00:19if you think about it.
00:21I think about your two
00:21lines. Imagine I have a
00:23line here and a line
00:25here and let's say
00:28This guy has a direction
00:29vector like this, so parallel
00:31to the line. And this
00:33guy has a direction vector
00:35like this, parallel to the
00:39line. Imagine I, let's pick
00:44up this vector, I'm gonna
00:47pick up this vector, I
00:48can pick up the lines,
00:50and I put these together
00:51like that. Well look, that
00:54angle there is the
00:56same as the angle between
00:57the two lines. If I
01:00drew it perfectly, if I
01:03drew it perfectly parallel that
01:04is, but that's pretty good.
01:07So yeah, once I find
01:08the angle between the two
01:09direction vectors, I can find
01:11the angle between the two
01:11lines. Now the only thing
01:13is where the angle between
01:15two vectors, if I have
01:18the angle between the two
01:20vectors, that's this angle. It's
01:22the angle between these two.
01:24But the angle between two
01:25lines could be, let me
01:28move this here. The angle
01:30between two lines could be,
01:34it could be this or
01:40this, there's two angles between
01:44two lines. This one and
01:46this one, the acute one
01:47and the obtuse one. Unless
01:49they meet at right angles
01:50in which case they're both
01:51right angles.
01:52So note my question says
01:53find the acute angle between
01:55the lines but you may
01:56get asked find the obtuse
01:57angle between two lines or
01:59you could just ask to
02:02find an angle between the
02:03two lines. Normally they do
02:05specify which one they want
02:06but just make sure you
02:08read the question. Okay, so
02:11let's just do it. I'm
02:12not going to teach you
02:13anything new here because you've
02:14already done angle between two
02:16lines but there's a formula
02:18and it is cost of
02:19theta.
02:20is equal to a dot
02:22b over the magnitude of
02:24a times the magnitude of
02:25b. That is in the
02:26formula booklet. What's a and
02:27what's b? Well, that's a
02:29and that's b. So a
02:31dot b is equal to
02:34a dot b. Let me
02:35just write it like this.
02:37a dot b is negative
02:38three, four, two dot b,
02:41which is two, three, three.
02:44Now you could ask me,
02:45well, why is that a
02:46and that b and not
02:46that a and that b?
02:48Well, it doesn't matter. It's
02:49the same thing. I could
02:50use that as A and
02:51that is B because A
02:52.B equals B .A. Anyway,
02:55this times this is negative
02:56six, or this dot this
02:58plus 12 plus six, which
03:02equals 12. And now I
03:05need the magnitude of A
03:07and the magnitude of B.
03:08So the magnitude of A,
03:11the magnitude of A is
03:13going to equal the square
03:16root
03:16of 3 squared plus 4
03:20squared plus 2 squared which
03:24is equal to the square
03:26root of 9 plus 16
03:30plus 4 which is 29
03:32and then the magnitude of
03:34B is equal to the
03:37square root of 2 squared
03:39plus 3 squared which is
03:439 plus 9 is 18
03:44plus 4 is 22, it's
03:47root 22. So this is
03:49equal to 12 over the
03:52square root of 29 times
03:54the square root of 22.
03:56This is cos theta, how
03:58do I find theta? Well,
04:02theta, I need my calculator
04:04and it is the inverse
04:09cos, where's my calculator gone.
04:12should have opened this before.
04:15So if this is cost
04:16of theta, the inverse cost
04:18of theta will give me
04:19the angle. Now remember, they've
04:23asked for the acute angle.
04:25So I actually don't know
04:27if this is going to
04:29give me an acute angle
04:31or a up shoe angle.
04:35But actually because it is
04:38because it is
04:40I do know it's gonna
04:42give me an acute angle,
04:44but if this was negative
04:45and it was giving me
04:46an obtuse angle then Well,
04:53just be careful Depending on
04:55what it what it gives
04:56you if it gives you
04:57an obtuse angle You need
04:59to do 180 minus the
05:00obtuse angle to give to
05:01get you the acute angle
05:03Okay, let me just Do
05:07this calculate
05:08Here I'm going to do
05:11inverse costs. So inverse costs
05:13of 12 over the square
05:21root of 29 times the
05:27square root of 22. I'm
05:30in degrees. Again, he didn't
05:32tell me which I wanted
05:33degrees. Our ratings often for
05:35vectors we use degrees.
05:36So I'm just going to
05:37use degrees here, if you
05:38ask for radians, fine, give
05:39it an radians. 61 .6351.
05:43So this is 61 .6351
05:47degrees. That is the acute
05:52angle. If you do this,
05:56and this is negative or
05:58whatever, and you get an
05:58obtuse angle, or even if
06:01you said, find the obtuse
06:02angle. So imagine this question,
06:04it's find the obtuse angle.
06:04you do all this as
06:06normal you get 61 .6351
06:08you recognize that this is
06:11your 61 .6351 degree angle
06:14this is the acute one
06:16which means this pink one
06:18is 180 minus 61 .6351
06:23and obviously make that calculation
06:28and that's the angle okay
06:31that's it fairly straight
06:33forward without a doubt the
06:35big takeaway here is the
06:36angle between two lines is
06:38the angle between the direction
06:40vectors. That's it. See you
06:43in the next video.