Thread: Vector help please.

Line 1 = -4i + j +3k + s(i + 5j - 2k)
Line 2 = 3i - 7j + 9k + t(2i - 3j + k)

The lines are skew.

Question: Find the position vector of the point C on line 2 such that ∠ABC = 90°.

Annnd...i have no idea how...I've tried random things but nothing works.
The answer is -7i + 8j + 4k

Any help or prods in the right direction would be appreciated.
Thank-you very much!

Originally Posted by AshleyT

Line 1 = -4i + j +3k + s(i + 5j - 2k)
Line 2 = 3i - 7j + 9k + t(2i - 3j + k) The lines are skew.
Question: Find the position vector of the point C on line 2 such that ∠ABC = 90°.

You have failed to tell us anything about A or B.

Originally Posted by Plato

You have failed to tell us anything about A or B.

O, sorry!
A and B have position vectors
4i + 1j + 3k
and
3i + 6j + k
respectively

Originally Posted by AshleyT

O, sorry!
A and B have position vectors
4i + 1j + 3k
and
3i + 6j + k
respectively

Then A and B are not on line 1 or line 2? And, in fact, line 1 has nothing to do with this problem? C, since it is on line 2, can be written with position vector (3+2t)i- (7+ 3t)j+ (9+ t)k.

Then the vector from C to B is (3+2t- 3)i- (7+ 3t- 6)j+ (9+t- 1)k= 2ti- (1+ 3t)j+ (8+ t)k. The vector from A to B is (3- 4)i+ (6- 1)j+ (1- 3)k= -i+ 5j- 2k. The angle ABC will be 90 degrees if and only if those two vectors are orthogonal which itself is true if and only if their dot product is 0:
-1(2t)- 5(1+ 3t)- 2(8+ t)= -25t- 21= 0 or t= -21/25. That does NOT give the C that you say is the answer. Are you sure you have copied everything correctly?

Sorry, this is the entire question...i gave Line 1 because i thought it was needed.

I'll attach the exam paper because i can't copy and paste very well from this laptop. Its question 7.

Thankyou very much for your reply!

So from the question paper it seems that you have copied the coordinates of both A and B incorrectly. That might account for not being able to get the answer right.

Well it was more that i never even knew where to start lol!
I kinda understand it now though, im going to try again tomorrow, vectors give me a headache!