Vectors question

I've been given the following. The angle ACO is 15 degrees and BCO is 30 degrees.

Find the lengths of OB and OC, done that

1+\frac{1}{3}(2\sqrt3)

and

2+\sqrt3

respectively. Then I'm asked to find the coordinates of vectors AB AC and BC.

Now I'm not too sure on this part, as I haven't been given any points. All I've managed to do is rewrite it as OB-OA etc.

Eh. I'd just find the length of OA and go from there.

Assuming A, B, and C are on the x, y, z axis respectively, vector OA = (OA,0,0), vector OB = (0,OB,0), and vector OC = (0,0,OC).

Reply 2

Music99

OP

4

Original post by aznkid66

Eh. I'd just find the length of OA and go from there.

Assuming A, B, and C are on the x, y, z axis respectively, vector OA = (OA,0,0), vector OB = (0,OB,0), and vector OC = (0,0,OC).

So I've got the length of OA OB and OC (OA is 1 shown on the diagram), but then how do I find the coordinates? is AB just (0,1,0)-(1,0,0)?

Reply 3

aznkid66

1

As you said, AB=-OA+OB.

If OA lies on the ? axis and has a magnitude of 1, then what're the three components of vector OA?
If OB lies on the ? axis and has a magnitude of 2/rt3+1, then what're the three components of vector OB?

(I only use ? because your diagram doesn't clearly show exactly which points lies on which axis.)

Reply 4

Music99

OP

4

Original post by aznkid66

As you said, AB=-OA+OB.

If OA lies on the ? axis and has a magnitude of 1, then what're the three components of vector OA?
If OB lies on the ? axis and has a magnitude of 2/rt3+1, then what're the three components of vector OB?

(I only use ? because your diagram doesn't clearly show exactly which points lies on which axis.)

Yeah sorry diagram is rubbish. A lies on the x axis B on the y C on the z.

so the components of OA are (1,0,0) OB are (1,2/rt3+1,0) OC (0,0,2+root3) ?

Reply 5

aznkid66

1

Original post by Music99

so the components of OA are (1,0,0) OB are (0,2/rt3+1,0) OC (0,0,2+root3) ?

Fixed that for ya, so yup :P
So you see how to arrive at the answers now, right?

Reply 6

Music99

OP

4

Original post by aznkid66

Fixed that for ya, so yup :P
So you see how to arrive at the answers now, right?

:P cheers. Yeah was just being a bit silly, might quote you again in a bit if I get stuck on anymore if you don't mind?

Reply 7

aznkid66

1

Original post by Music99

:P cheers. Yeah was just being a bit silly, might quote you again in a bit if I get stuck on anymore if you don't mind?

Sure, no problem ^^

Reply 8

Music99

OP

4

Original post by aznkid66

Sure, no problem ^^

Find the area of the triangle ABC I did that got 19.3 (3sf), Then I'm asked to find the coordinates of M, where the normal from the origin meets the plane of the triangle ABC. Is that the point that just passes through C on my diagram?