# Category Archives: Vectors

# STEP 2/2012/7

# STEP 2/2011/5

# STEP 1/2016/6

# STEP 2/2017/8

# STEP 2/2009/8

The non-collinear points A, B, C have position vectors **a**, **b**, **c** respectively. The points P and Q have position vectors **p** and **q**, respectively, given by

**p** = λ **a** + (1 − λ)**b**

**q** = μ **a** + (1 − μ)**c**

where 0 < λ < 1. Draw a diagram showing A, B, C, P and Q

Given that CQ.BP = AB.AC, find μ in terms of λ, and show that, for all values of λ, the line PQ passes through the fixed point D, with position vector **d** given by

**d = − a + b + c**

What can be said about the quadrilateral ABDC?

# STEP 2/2008/8

The points A and B have position vectors **a** and **b**, respectively, relative to the origin O. The points A, B, and O are not collinear. The point P lies on AB between A and B such that

Write down the position vector of P in terms of **a**, **b**, and λ

Given that OP bisects the angle AOB, determine λ in terms of *a* and *b*, where

*a* = |**a**| and *b* = |**b**|

The point Q also lies on AB between A and B, and is such that AP=BQ. Prove that

OQ^{2} − OP^{2} = (b-a)^{2}

# Distance from a point to a line using vectors – video clip

# Don’t do as the book says, FP3 vectors

Line where two planes meet; shortest distance from point to line; distance between two parallel lines. Continue reading