Vectors in geometry

Vector a is drawn on this grid.

Write vector a as a column vector.

Work out. +

On the grid below, draw

Vector a is drawn on this grid.

Write vector a as a column vector.

A vector is drawn on this grid.

Write this vector in terms of a.

Vector a and vector 2b are drawn on this grid.

Write vector a as a column vector.

Write a column vector that is different in direction but has the same length as vector a.

On the grid below, draw the vector a – b.

Work out.

+

- 2

Vector a = and vector b = .

On the grid, draw vector a.

On the grid, draw vector a + b.

OABC is a parallelogram.

Find the following vectors in terms of a and c. Give your answers in their simplest form.

Line CN is extended to reach point P, such that =

Show, using vectors, that OAP is a straight line.

Vector a is drawn on this grid.

Write vector a as a column vector.

On the grid above, draw the vector – a.

Vectors a and 4 b are drawn on the grid.

Write vector a as a column vector.

Find vector b as a column vector.

Vectors a and 4 b are drawn on the grid.

Write vector a as a column vector.

Find vector b as a column vector.

Vector m = and vector n = . Vector 2m + n is parallel to .

Find the value of k.

Vector a = and vector b = .

Find the values of k and n so that

Gavin starts to draw a diagram to show that a + 2b = .

Complete Gavin’s diagram.

The diagram shows triangle OAB and points C and D.

Show, using vectors, that OCD is a straight line.

Triangle A and triangle B are drawn on the coordinate grid.

Draw the image of triangle A after a rotation of 180 ° about (0, 0).

Draw the image of triangle A after a translation by the vector .

Describe fully the single transformation that maps triangle A onto triangle B.

b is a vector. Given that b + is parallel to , find two possible answers for b.

Given that

find the value of m and the value of n.

Find the values of h and k.

Triangle ABC is drawn on a coordinate grid.

Use the diagram to complete this vector sum.

Give a reason why the answer to the sum could be written down without doing any working.

Work out.

+

- 2

Two vectors, a and b, are shown on the 1 centimetre grid below.

Show that the vector a + 2 b has length 7 cm. You may use the grid below.

ABCD is a parallelogram.

Write down simplified expressions in terms of a and b for

Prove that and are parallel.

Triangle A and triangle B are drawn on the coordinate grid.

Translate triangle A by vector .

Describe fully the single transformation that maps triangle A onto triangle B.

Vector a = , vector b = .

On each grid below, draw a vector to represent

(i) 2a,
(ii) a + b.

Emma says that if she draws vector a and vector b they will be the same.

Explain why this is incorrect.

c = . Find the value k so that ka - b = c.