Vectors: notation and journeys

a = (3, 5) and b = (2, −1).

Work out a + b as a column vector.

a = (4, −3) and b = (1, 6).

Work out 2a + b as a column vector.

p = (5, 2) and q = (3, −4).

Work out p − 2q as a column vector.

a = (−2, 5) and b = (3, −1).

Work out 3a − 2b as a column vector.

OAB is a triangle. OA = a and OB = b.

Write down, in terms of a and b, the vector AB.

P is the point (3, 4) and Q is the point (-1, 6).

Write PQ as a column vector.

a = (3, −1) and b = (−1, 2).

On the grid, draw and label the vector a + 2b.

k(2, −3) + (5, 1) = (13, m)

where k and m are numbers.

Find the value of k and the value of m.

OABC is a parallelogram. OA = a and OC = c.

Write down, in terms of a and c, the vectors

1. OB
2. AC
3. BA

Work out the magnitude (length) of each of these vectors.

1. (5, 12)
2. (4, -7). Give your answer correct to 3 significant figures.

p = (6, -9) and q = (-2, 3).

Show that p and q are parallel.

A is the point (1, 2) and B is the point (5, 8).

ABC is a straight line and BC = 12AB.

Work out the coordinates of C.

The points are in the order A, B, C, so C lies beyond B.

m(2, 1) + n(1, 3) = (4, 7)

where m and n are numbers.

Find the value of m and the value of n.

The vector (4, k) is parallel to the vector (6, 9).

Work out the value of k.

a = (2, 1) and b = (1, −2).

On the grid, draw and label the vector 2a − b.

a = (1, 2) and b = (3, -1).

(9, 4) = ma + nb, where m and n are numbers.

Find the value of m and the value of n.

AB = 2a + 4b and BC = 3a + 6b.

Show that A, B and C lie on a straight line.

OAB is a triangle. OA = a and OB = b.

P is the point on AB such that AP : PB = 2 : 1.

Express OP in terms of a and b. Give your answer in its simplest form.

OABC is a trapezium. OA = a and OC = c.

CB is parallel to OA and CB = 2a.

M is the midpoint of AB.

Find OM in terms of a and c. Give your answer in its simplest form.