## 2001 Paper 2 Q. 4

### gary

Posted 16 May 2005 - 10:37 AM

I have worked out the angle for this question I got 108.5

However, the answer is 71.5 which is 180-108.5 = 71.5.

I don't understand why this is can someone explain.

### Dave

Posted 16 May 2005 - 12:22 PM

well the equation you should be using is

cos [ theta] = BA.BC/mod(BA)*mod(BC)

BA = (6,-5,1)
BC(4,0,-6)

BA.BC = 18

mod (BA) = 62
mod(BC) = 52

that gives the answer you want

### gary

Posted 16 May 2005 - 01:06 PM

Yeah I worked that out but

AB.BC is -18.

### dfx

Posted 16 May 2005 - 01:34 PM

You need angle ABC, so you gota work out BA.BC, not AB.BC, since both the vectors should be heading outwards form the centre of the angle which ur working out.

### gary

Posted 16 May 2005 - 01:38 PM

Yeah that is what I have done AB= b-a etc.

### dfx

Posted 16 May 2005 - 01:39 PM

Na-uh. AB is NOT equal to BA. Its actually the negative. so AB is b -a but BA is a - b. Which probably explains why you're getting -18 when its +18.

### gary

Posted 16 May 2005 - 01:43 PM

Ok I believe you but I don't understand why they have to be facing outwards.

### dfx

Posted 16 May 2005 - 02:08 PM

Cause the dot product of two vectors gives you the angle BETWEEN the two vectors. The angle between the two vectors is the angle between the origin of both vectors. Have a look at the attached diagram. The one the left is the correct way for finding the angle ABC. The one on the right is what you got.

lol, or if you want it the easy way, beats me. Just do what they say

### dfx

Posted 16 May 2005 - 02:10 PM

Someone just double check that, cause what I've drawn is AB.AC not AB.BC... hmmmm....

### Chünz

Posted 16 May 2005 - 02:34 PM

You will have done what I did... I took AB.BC

Instead, you have to take BC.BA

When you do this, you will notice that you get +18 instead of -18. Then, using 62 X 52, you will get 71.52

### Dave

Posted 16 May 2005 - 03:52 PM

look at the diagram

The angle is at point B so you must do a vector from B to A and from B to C

What you have done is from A to B and from A to C so you have measured the wrong angle