Free Printable Unit 18 - Vectors and Geometric Proof

1.

a)

$\left(3\ 4\right)\ and\ \left(-5\ 8\right)$

b)

$\left(3\ 4\right)\ and\ \left(5\ -8\right)$

c)

$\left(3\ 4\right)\ and\ \left(-6\ 8\right)$

d)

$\left(5\ 4\right)\ and\ \left(6\ 8\right)$

2.

a)

$\left(4\ \ 2\right)$

b)

$\left(4\ -2\right)$

c)

$\left(2\ -1\right)$

d)

$\left(-2\ 1\right)$

3.

a)

$\overrightarrow{MB}=\frac{1}{2}a\ and\ \overrightarrow{MN}=\frac{1}{2}a+\frac{1}{2}c$

b)

$\overrightarrow{MB}=\frac{1}{2}a\ and\ \overrightarrow{MN}=-\frac{1}{2}a-\frac{1}{2}c$

c)

$\overrightarrow{MB}=-\frac{1}{2}a\ and\ \overrightarrow{MN}=\frac{1}{2}a-\frac{1}{2}c$

d)

$\overrightarrow{MB}=\frac{1}{2}a\ and\ \overrightarrow{MN}=\frac{1}{2}a-\frac{1}{2}c$

4.

a)

$\sqrt{29}$

b)

$\sqrt{21}$

c)

$\sqrt{-29}$

d)

$5.4$

5.

a)

$a+b,\ 2\left(a+b\right),3a+3b$

b)

$a+b,\ 2\left(a+b\right),3a+3b,\ 2a+2b$

c)

$a+b,3a+3b,\ 2a+2b$

d)

$2\left(a+b\right),3a+3b,\ 2a+2b$

6.

Write the vector $\overrightarrow{SR}$ in terms of a and b

a)

b-a

b)

-b + a

c)

a + b

d)

-a + b

7.

$T\ is\ \frac{1}{3}along\ the\ vector\ \overrightarrow{RS},\ write\ the\ vector\ \overrightarrow{RT}\ in\ terms\ of\ a\ and\ b$

Write your question here

a)

$\frac{1}{3}\left(-b+a\right)$

b)

$\frac{1}{3}\left(a-b\right)$

c)

$\frac{2}{3}\left(-b+a\right)$

d)

$\frac{2}{3}\left(-a+b\right)$

8.

write the vector $\overrightarrow{PQ}$ in terms of p and q

a)

2p - 3q

b)

2p + 3q

c)

-2p + 3q

d)

3q - 2p

9.

$R\ is\ \frac{2}{5}\ along\ the\ vector\ \overrightarrow{PQ},\ Calculate\ the\ vector\overrightarrow{\ OR}\ in\ terms\ of\ p\ and\ q$

a)

$\frac{6}{5}p\ +\frac{6}{5}q$

b)

$\frac{6}{5}p\ -\frac{6}{5}q$

c)

$\frac{14}{5}p\ +\frac{6}{5}q$

d)

$2p-\frac{4}{5}p+\frac{6}{5}q$

10.

a)

$\overrightarrow{AE}=4q\ and\ \overrightarrow{AC}=-q+p$

b)

$\overrightarrow{AE}=2q\ and\ \overrightarrow{AC}=q-p$

c)

$\overrightarrow{AE}=2q\ and\ \overrightarrow{AC}=-q+p$

d)

$\overrightarrow{AE}=2q\ and\ \overrightarrow{AC}=q+p$

Unit 18 - Vectors and Geometric Proof

Total questions: 10

Worksheet time: 20mins

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