The vector and the vector are shown on the grid.
On the grid, draw and label vector
Work out as a column vector.
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The vector and the vector are shown on the grid.
On the grid, draw and label vector
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Work out as a column vector.
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is a triangle.
Find in terms of and .
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is the point on such that
Find in terms of and .
Give your answer in its simplest form.
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is a parallelogram.
is the point on such that
Write down, in terms of and , an expression for
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Express in terms of and.
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is a triangle.
is the midpoint of .
is the midpoint of .
Show that is parallel to .
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is a quadrilateral.
Express in terms of and .
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is the point onsuch that
and .
Prove that
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Circle the vector that translates the point (–2, 7) to the point (3, –1)
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Here is vector .
Circle the column vector that represents .
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and
Work out
Circle your answer.
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and
Circle the vector
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and
Circle the vector
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Here are two vectors.
Find, as a column vector, .
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and are regular hexagons each with centre .
is an enlargement of , with centre and scale factor 2
Write the following vectors, in terms of and .
Simplify your answers.
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is a regular hexagon.
and are straight lines.
Find in terms of and .
Give your answer in its simplest form.
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Vectors and 4b are drawn on the grid.
Write vector as a column vector.
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Find vector b as a column vector.
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Vector and vector
Gavin starts to draw a diagram to show that
Complete Gavin’s diagram.
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is a vector.
Given that is parallel to , find two possible answers for .
or
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Vector , vector .
On each grid below, draw a vector to represent
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Emma says that if she draws vector and vector they will be the same.
Explain why this is incorrect.
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Vectors a, b, c, d and e are drawn on an isometric grid.
Write each of the vectors c, d and e in terms of a and/or b.
c = ....................
d = ....................
e = ....................
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is a triangle.
is a point on .
Find the vector , in terms of and .
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is the midpoint of .
is the midpoint of .
Show that is a straight line.
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is a trapezium.
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is the point on such that = 1 : 3
Find in terms of and .
Give your answer in its simplest form.
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What does your answer to part (b) tell you about the position of point ?
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is a triangle.
is the point on such that
Show that is parallel to the vector .
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and
is the midpoint of .
Write in terms of and .
Give your answer in its simplest form.
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is the midpoint of .
is the point on such that = 2 : 1
Show that is a straight line.
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is a quadrilateral.
is the point on such that
Prove that
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is a triangle.
is the point on such that
where is a scalar quantity.
Find the value of .
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In triangle
is the midpoint of
Work out in terms of and .
Give your answer in its simplest form.
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is a straight line.
Circle the vector
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Work out .
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Show that is parallel to .
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Is a straight line?
Show working to support your answer.
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is a triangle.
The midpoint of is .
is a point on .
Find the ratio .
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is a triangle.
The point lies on such that
The point lies on such that
Using a vector method, prove that is a trapezium.
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The diagram shows parallelogram .
The point has coordinates (5, 8)
Work out the coordinates of the point .
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The point has coordinates (63, 211)
Use a vector method to prove that is a straight line.
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The diagram shows triangle
is the midpoint of .
is the midpoint of .
is the point on such that
and
Express, in terms of and ,
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State, giving reasons, two different geometric facts relating and
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Given that
find the value of and the value of .
= .......................
= .......................
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Two vectors, a and b, are shown on the 1 centimetre grid below.
Show that the vector a + 2b has length 7cm.
You may use the grid below.
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Vector , vector .
Find the value so that
= .....................................................
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P, Q, R and S are the midpoints of OX, XY, YZ and OZ respectively.
, and .
Show that is parallel to .
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is a parallelogram.
is the point such that
The point divides in the ratio
Write an expression for in terms of and .
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Prove that is a straight line.
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is a straight line.
Express in terms of and .
Give your answer in its simplest form.
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is a parallelogram.
is the midpoint of .
is the midpoint of .
Show that is a straight line.
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is a parallelogram.
is the midpoint of the line .
is a straight line so that
Given that
find the value of
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and are straight lines.
is the midpoint of .
where is a scalar quantity.
Given that is a straight line, find the value of .
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and are straight lines.
is the midpoint of .
is the midpoint of .
where is a scalar quantity.
Given that is a straight line, find the value of .
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is a quadrilateral.
Express in terms of and/or .
Give your answer in its simplest form.
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is the midpoint of .
is the point on such that
is a straight line.
Work out the value of .
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In the diagram
Show that
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Is a straight line?
Show working to support your answer.
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Here is quadrilateral .
is a point on where
is a point on where
Is parallel to
Show working to support your answer.
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is a pentagon.
Show that is a parallelogram.
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The diagram shows triangle
is the point on such that
is the midpoint of
is the point of intersection of and
Using a vector method, find as a simplified expression in terms of and
Show your working clearly.
= ...................................
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is a trapezium.
is the midpoint of
is the point such that and are straight lines.
Given that
use a vector method to find the value of
....................................................
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Vector m= and vector n =
Vector 2m + n is parallel to
Find the value of .
.........................................
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The diagram shows triangle OAB and points C and D.
= 3and = 3b.
C lies on AB such that AC = 2CB.
D is such that = + 2 + b.
Show, using vectors, that OCD is a straight line.
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is a parallelogram.
and .
is the midpoint of .
is the midpoint of .
Prove that and are parallel.
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