Vectors

mpx

drawing

Given that and
(a) Find .
(b) The vector is parallel to the vector . Find .
Find and such that .
The points and C have coordinates and respectively.
(a) Write down the vectors and .
(b) Write down an equation linking vectors and .
Find a unit vector in the direction of .
(d) A fourth point D is positioned so that ABCD is a trapezium with AD parallel to BC and .

Find the coordinates of D .
3. OABC is a quadrilateral. Relative to point O , points

and C have position vectors

respectively. The midpoints of

and OA are the points

and S respectively.
(a) Show P has position vector

(b) Hence write down the position vectors of

and S .

Show that

.
(d) State, with a reason, what geometrical shape PQRS is.
4. Relative to the point O , points

and C have position vectors

and

respectively. M is the midpoint of BC .

(a) You are given that

. Explain why O , A and M must form a straight line.
(b) Hence find the value of

.
5. The corners of triangle PQR lie on a circle.

and

.
(a) Find the lengths of

and PR and explain how this shows that the triangle is rightangled.
(b) Hence find the area of the circle.

Total 40 marks

drawing