You are Here: Home >< Maths

# C4 vectors watch

Q1) Referred to a fixed origin, the line L1 has the equation r=12i+15j+k+s(2i+j+k) and the line L2 has the equation r=i+j-2k+t(3i-k)

a) Show that the lines L1 and L2 intersect and find the position vector of A, their point of intersection

b) Find, to the nearest degree, the acute angle between the lines L1 and L2

The point B with position vector 16i+7j+3k lies on the line L1. The point C with position vector 22i+j-9K and the point D both lie on the line L2.

c)Given that BD is perpendicular to AC, find the position vector of D

d)Hence, or otherwise, prove that ?ABC is isosceles

Thank you for the help in advance....I REALLY APPRECIATE IT!!
2. (a) If the lines intersect, there must be a point that lies on both of them. That point will lie on L1 for some value of s and L2 for some value of t. So set up simultaneous equations for the coefficients of I J and K.

(b) have you just done scalar product?
3. (Original post by ian.slater)
(a) If the lines intersect, there must be a point that lies on both of them. That point will lie on L1 for some value of s and L2 for some value of t. So set up simultaneous equations for the coefficients of I J and K.

(b) have you just done scalar product?
Thanks, I've managed to do parts a) and b) but can't do c) and d)

Yes the scalar product --> a.b= [modulas of a x modulas of b] cos theta ??
4. (Original post by Air18)
Thanks, I've managed to do parts a) and b) but can't do c) and d)

Yes the scalar product --> a.b= [modulas of a x modulas of b] cos theta ??
So if the scalar product of two vectors (worked out by multiplying coefficients and adding) is zero, then the lines are perpendicular.

You can work out AC. You know D lies on L2 and can work out BD - which will have a 't' in it. If you set AC.BD to zero you can find t and hence D.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 27, 2011
Today on TSR

### He lied about his age

Thought he was 19... really he's 14

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams