Vectors2

1. P is the point (0,2,4), Q(1,3,5) and R(-2,0,-4). If represents a and represents b use components to calculate a.b

2. P is the point (1,2,-3) and Q is (11,-3,7). PQ is divided internally at R in the ratio 3:2.

represents a and represents b. Calculate

a) the coordinates of R

b) the components of a and b

c) a.b

3. Show that the angle between the vectors I – j + 2k and I + k is exactly

4 Find the coordinates of the point R which divides the line joining P(-2,-1,3) and Q(4,2,3) in the ratio 2:1

If S is the point (3,-1,1), show that angle PRS is a right angle by

a) the scalar product

b) the converse of Pythagoras' Theorem

5. Given that the angle between the vectors 2i – j + 3k and i + 3j –pk is , find p.