You are Here: Home >< Maths

# C4? VEctors question Help Plz! watch

1. Hi every1, was doing maths hw on vectors and came across one question which i found difficult! could someone help please! I will post all parts to the qu - thanks in advance!

The postition vectors of three points, A, B and C with respect to a fixed origin O are:
(2i-2j+k), (4i+2j+k) and (i+j+3k) respectively.

a) Write down unit vectors in the direction of the lines CA and CB and calculate the size of angleACB.

The midpoint of AB is M.
b) find a vector equation of the straight line passing through C and M
c) show that AB and CM are perpendicular.
d)find the position vector of the point N on the line CM such that angleONC =90degrees.

Any help on any part would be greatly appreciated!!
2. a)

CA = (2-1)i+(-2-1)j+(1-3)k = i-3j-2k

unit vector: sqrt(1^2+3^2+2^2)(CA) = rt14(i-3j-2k)

CB = (4-1)i+(2-1)j+(1-3)k = 3i+j-2k

you can do the unit vector...

CA.CB = (1)(3) + (-3)(1) + (-2)(-2) = |CA||CB|cosx

x = acos(4/(rt14)(rt14)) = acos(2/7) = 73.4
3. Thanks, the answer i got for first part was diff to urs...

CA = i - 3j - 2k - that i worked out the same.

lCAl = sqrt(1+9+4)
=sqrt14
therefore unit vector = (i-3j-2k)/sqrt14

is that not correct?
4. oh yeah. i can't add.
5. i got 73.4?

CA.CB = 3 +(-3)+4
=4
cos x = 4/(sqrt14)(sqrt14)
=4/14
x = 73.4?

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: February 5, 2006
Today on TSR

### University open days

• Southampton Solent University
Sun, 18 Nov '18
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '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