Vectors as Letters

In this worksheet, students must use letter notation to answer questions on vectors.

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Difficulty level:

QUESTION 1 of 10

Look at the following vector diagram in which M and N are the midpoints of AB and BC respectively.

To get from C to A you can either do a backwards q or an s followed by a backwards p.

To get from M to N you can also do -½p + q + ½s.

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

-s

2s

r - 2s

r - s

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

-s

2s

s - r

r - s

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

-s

2s

r - 2s

s - r

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

-s

2s

s - r

-r - s

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of p, q, r and s, for the vector

-s

½s

2s

½s

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of p, q, r and s, for the vector

-p

½p

-½p

½p

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of p, q, r and s, for the vector

½p - ½s

½p + ½s

-½p + s

½ps

L, M and N are the midpoints of AD, AB and BC respectively.

Select an expression, in terms of r, s, t and u, for the vector

½t - ½s

½s - ½t

-½t + s

½s + ½t

L, M and N are the midpoints of AD, AB and BC respectively.

Select an expression, in terms of r, s, tand u, for the vector

½s - ½r

½s - ½t

-½r + s

-r + s

L, M and N are the midpoints of AD, AB and BC respectively.

Select all the expressions, in terms of r, s, tand u, for the vector

½t - u - ½r

½s - u - ½t

½t - u - ½s

-½t - s + ½r

• Question 1

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

2s
EDDIE SAYS
Two lots of s.
• Question 2

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

s - r
EDDIE SAYS
Go from D to O and then from O to C, which is -r and then s.
• Question 3

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

s - r
EDDIE SAYS
This is the same vector as D to C.
• Question 4

ABCD is a parallelogram.

The diagonals intersect at O.

Select an expression, in terms of r and s, for the vector

-r - s
EDDIE SAYS
Go from C to O and then from O to B, which is -s and then -r.
• Question 5

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of p, q, r and s, for the vector

½s
EDDIE SAYS
This is half of s.
• Question 6

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of p, q, r and s, for the vector

-½p
EDDIE SAYS
This is half of p but backwards.
• Question 7

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of p, q, r and s, for the vector

½p - ½s
EDDIE SAYS
This is the same as M to B and then B to N, which is half of p and then half of -s.
• Question 8

L, M and N are the midpoints of AD, AB and BC respectively.

Select an expression, in terms of r, s, t and u, for the vector

½s + ½t
EDDIE SAYS
This is the same as M to B and then B to N, which is half of s and then half of t.
• Question 9

L, M and N are the midpoints of AD, AB and BC respectively.

Select an expression, in terms of r, s, tand u, for the vector

½s - ½r
EDDIE SAYS
This is the same as L to A and then A to M, which is half of -r and then half of s.
• Question 10

L, M and N are the midpoints of AD, AB and BC respectively.

Select all the expressions, in terms of r, s, tand u, for the vector

½t - u - ½r
-½t - s + ½r
EDDIE SAYS
There are two routes.
N to C then C to D then D to L, which is ½t - u - ½r
N to B then B to A then A to L, which is -½t - s + ½r
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