Magnitude & direction of a vector

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.

Find the position vector of the point B

find the exact value of x

Figure 3 shows the triangle OAB where OA = 12a and OB = 6b M is the midpoint of OA and N is the midpoint of AB.

The point P on BM is such that BP: BM = 2: 3

Simplifying your answer, find, in terms of a and b

(i) BM (ii) OP

Hence show that O, P and N are collinear.

Given that | a| = | b | = 1 cm and that AOB = 70°

find the length, in cm to 3 significant figures, of OP.

[ Cosine rule: a² = b² + c² − 2bc cosA ]

Find AB as a column vector.

Calculate the modulus of AB