Vector arithmetic

Give your answer in the form d c where c and d are integers

such that c 0 and d 0

Show all your working.

M is the midpoint of OA

N is the point on AB such that AN: NB = 4:1

Given that the point X is such that OXN and MXB are straight lines,

find a simplified expression for in terms of a and b

Find the position vector of the point B

For the two non-zero, non-parallel vectors a and b

5(3 a – b) – p (a + 2 b) = q b

where p and q are scalars.

Find the value of p and the value of q

The position vector of A is 83

The point B has coordinates (2, 4)

Find AB →

The diagonals AC and BD meet at the point E

Find as a column vector BC →

The point E has coordinates (6, 4)

Given that AE:AC = 3: 5

find the coordinates of the point A

Given that ABCD is a kite,

find the coordinates of the point D

Figure 2 shows the triangle OAB with OA = 2a and OB = 3b

Find CD in terms of a and b.

The point P is such that ODBP is a straight line and AP is parallel to CD.

Find OP in terms of b.

The point Q is such that CD = DQ

Show that A, B and Q are collinear.

Find AB as a column vector.

Calculate the modulus of AB