The vector and the vector
are shown on the grid.

On the grid, draw and label vectorÂ
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 vectorÂ
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Work out as a column vector.
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is a triangle.
Find in terms ofÂ
and
.
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is the point onÂ
such thatÂ
Find in terms ofÂ
and
.
Give your answer in its simplest form.
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is a parallelogram.
is the point on
such thatÂ
Write down, in terms of and
, an expression forÂ
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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 toÂ
.
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 is a quadrilateral.
Express in terms ofÂ
and
.
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is the point on
such that
andÂ
Prove that Â
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Here are two vectors.
       Â
Find, as a column vector,Â
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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.
i)
[1]
ii)
[2]
iii)
[2]
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 is a regular hexagon.
andÂ
are straight lines.
Find in terms ofÂ
and
.
Give your answer in its simplest form.
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Here is vector .
Circle the column vector that represents .
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andÂ
Work out
Circle your answer.
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Vectors and
are drawn on the grid.
Write vector as a column vector.
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Find vector as a column vector.
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Vector and vectorÂ
Gavin starts to draw a diagram to show thatÂ
Complete Gavin’s diagram.
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 is a vector.
Given that is parallel toÂ
, find two possible answers for
.
orÂ
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Vector , vectorÂ
.
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.
i) Find in terms ofÂ
and
[1]
ii) Find in terms of
and
Give your answer in its simplest form.
[1]
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is the point onÂ
such that
= 1 : 3
Find in terms ofÂ
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 thatÂ
Show that is parallel to the vectorÂ
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andÂ
is the midpoint of
.
Write in terms ofÂ
and
.
Give your answer in its simplest form.
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is the midpoint of
.
is the point onÂ
such that
= 2 : 1
Show that is a straight line.
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 is a quadrilateral.
is the point on
such thatÂ
Prove thatÂ
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is a triangle.
is the point on
such thatÂ
whereÂ
is a scalar quantity.
Find the value of .
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is a triangle.
The midpoint of is
.
is a point on
.
Find the ratioÂ
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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 .
   Â
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 triangleÂ
is the midpoint of
.
is the midpoint of
.
is the point onÂ
such thatÂ
   and   Â
Express, in terms of and
,
i)
ii)
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State, giving reasons, two different geometric facts relating andÂ
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In triangle
is the midpoint of
     Â
Work out in terms of
and
.
Give your answer in its simplest form.
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is a straight line.
Circle the vectorÂ
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    Â
     Â
Work outÂ
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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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Given that
     Â
find the value of and the value of
.
= .......................
= .......................Â
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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 , vectorÂ
.
Find the value so thatÂ
= .....................................................
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P, Q, R and S are the midpoints of OX, XY, YZ and OZ respectively.
,Â
and
.
Show that is parallel to
.
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 is a parallelogram.
is the point such thatÂ
The point dividesÂ
in the ratioÂ
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 thatÂ
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
.
Â
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.
How did you do?
is the midpoint of
.
is the point on
such thatÂ
 is a straight line.
Work out the value of .
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The diagram shows triangle
  Â
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 thatÂ
andÂ
are straight lines.
Given that
use a vector method to find the value of
....................................................
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In the diagram
Show that Â
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Is a straight line?
Show working to support your answer.
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Here is quadrilateral .
   Â
   Â
and
are not parallel.
is a point on
where   Â
is a point on
where    Â
Is parallel toÂ
?
Show working to support your answer.
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is a pentagon.
Show that is a parallelogram.
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Vector m= and vector n =
Vector 2m + n is parallel toÂ
Find the value of .
.........................................
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The diagram shows triangle OAB and points C and D.
= 3
and
= 3
.
C lies on AB such that AC = 2CB.
D is such that = + 2
+
.
Show, using vectors, that OCD is a straight line.
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 is a parallelogram.
andÂ
.
is the midpoint of
.
is the midpoint of
.
Prove that and
are parallel.
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