Position vectors

The position vector of the point A is 0.5 i - 0.5 j.

Determine whether 0.5 i - 0.5 j is a unit vector.

Find the direction of 0.5 i - 0.5 j, giving your answer in degrees.

The position vector of the point B is 3.5i + cj, where c is a constant.

Given that = 5, determine the possible values of c.

It is given that ABCD is a quadrilateral. The position vector of A is i + j, and the position vector of B is 3 i + 5 j.

Find the length AB.

The position vector of C is p i + p j where p is a constant greater than 1.

Given that the length AB is equal to the length BC, determine the position vector of C.

The point M is the midpoint of AC.

Given that = , determine the position vector of D.

State the name of the quadrilateral ABCD, giving a reason for your answer.

Find, in terms of k, the length of OP.

Determine the value of k.

The points A and B have position vectors 3 i + 2 j and 4 i + 2 j - 5 k respectively.

Find the length of AB.

Point P has position vector p i - 3 k, where p is a constant. P lies on the circumference of a circle of which AB is a diameter.

Find the two possible values of p.

Points A, B and C have position vectors a, b and c relative to an origin O in 3-dimensional space. Rectangles OADC and BEFG are the base and top surface of a cuboid.

• The point M is the midpoint of BC.

• The point X lies on AM such that AX = 2 XM.

Find in terms of a, b and c, simplifying your answer.

Hence show that the lines OF and AM intersect.

A and B are fixed points in the x - y plane. The position vectors of A and B are a and b respectively.

State, with reference to points A and B, the geometrical significance of

the quantity | a - b |,

The circle P is the set of points with position vector p in the x - y plane which satisfy

State, in terms of a and b,

the position vector of the centre of P,

Enlarge

Find a cartesian equation of P.

The point A is such that the magnitude of is 8 and the direction of is 240°.

Show the point A on the axes provided in the Printed Answer Booklet.

Find the position vector of point A.

Give your answer in terms of i and j.

The point B has position vector 6 i.

Find the exact area of triangle AOB.

The point C is such that OABC is a parallelogram.

Find the position vector of C.

Give your answer in terms of i and j.

In this question the unit vectors i and j are in the directions east and north respectively.

A particle R of mass 2 kg is moving on a smooth horizontal surface under the action of a single horizontal force F N. At time t seconds, the velocity v ms^-1 of R, relative to a fixed origin O, is given by v = (pt² - 3t)i + (8t + q)j, where p and q are constants and p < 0.

Given that when t = 0.5 the magnitude of F is 20, find the value of p.

When t = 0, R is at the point with position vector (2 i - 3 j) m.

Find, in terms of q, an expression for the displacement vector of R at time t.

When t = 1, R is at a point on the line L, where L passes through O and the point with position vector 2 i - 8 j.

Find the value of q.

Find the exact length of AB.

Enlarge

Show that ABPQ is a parallelogram.