Oh, come on, vectors aren't all that bad. Are they?

Start

Congratulations - you have completed C4 Vectors quiz.

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1

Line $l_1$ has the equation $\mathbf{r}= \begin{pmatrix}1\\2\\2 \end{pmatrix} + \lambda \begin{pmatrix}4\\-3\\3\end{pmatrix}$.
Point $C$ has co-ordinates $(-1,3,0)$
Point $P$ lies on $l_1$ such that the vector $CP$ is perpendicular to $l_1$. What are the co-ordinates of $P$?

A

There is no such point.

B

$(2,3,0)$

C

$(3, 0.5, 3.5)$

D

$(-1, 3.5, 0.5)$

E

$(5,-1,5)$

Question 2

Point $A$ is at $\begin{pmatrix} 9\\ 0 \\ 3 \\ \end{pmatrix}$ and point $B$ is at $\begin{pmatrix} -3\\ 8 \\ -3 \\ \end{pmatrix}$. Which of the following is an equation of the line through $A$ and $B$?

Line $l_1$ has the equation $\mathbf{r}= \begin{pmatrix}1\\2\\2 \end{pmatrix} + \lambda \begin{pmatrix}4\\-3\\3\end{pmatrix}$.
Line $l_2$ has the equation $\mathbf{r}= \begin{pmatrix}5\\3\\3 \end{pmatrix} + \mu \begin{pmatrix}-12\\5\\-7\end{pmatrix}$.
What is the acute angle between $l_1$ and $l_2$?

A

None of these

B

167º

C

137º

D

13º

E

43º

Question 4

Point $A$ is at $\begin{pmatrix} 9\\ 0 \\ 3 \\ \end{pmatrix}$ and point $B$ is at $\begin{pmatrix} -3\\ 8 \\ -3 \\ \end{pmatrix}$. What is the distance $AB$?

A

$\sqrt{244}$

B

$109$

C

$244$

D

$26$

E

$71$

Question 5

Point $A$ is at $\begin{pmatrix} 9\\ 0 \\ 3 \\ \end{pmatrix}$ and point $B$ is at $\begin{pmatrix} -3\\ 8 \\ -3 \\ \end{pmatrix}$. What is the vector $AB$?

A

71º

B

$\sqrt{244}$

C

109º

D

$\begin{pmatrix}
-12 \\ 8 \\ -6 \\
\end{pmatrix}$

E

$\begin{pmatrix}
12\\ -8 \\ 6 \\
\end{pmatrix}$

Question 6

Line $l_1$ has the equation $\mathbf{r}= \begin{pmatrix}1\\2\\2 \end{pmatrix} + \lambda \begin{pmatrix}4\\-3\\3\end{pmatrix}$.
Line $l_2$ has the equation $\mathbf{r}= \begin{pmatrix}5\\3\\1 \end{pmatrix} + \mu \begin{pmatrix}-12\\5\\-5\end{pmatrix}$.
Where do lines $l_1$ and $l_2$ intersect?

A

$\begin{pmatrix}17\\-2\\8\end{pmatrix}$

B

You can't fool me, they don't!

C

$\begin{pmatrix}-7\\8\\-4\end{pmatrix}$

D

$\begin{pmatrix}1\\2\\2\end{pmatrix}$

E

$\begin{pmatrix}5\\-1\\5\end{pmatrix}$

Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
Get Results

There are 6 questions to complete.

←

List

→

Return

Shaded items are complete.

1

2

3

4

5

6

End

Return

You have completed

questions

question

Your score is

Correct

Wrong

Partial-Credit

You have not finished your quiz. If you leave this page, your progress will be lost.

Correct Answer

You Selected

Not Attempted

Final Score on Quiz

Attempted Questions Correct

Attempted Questions Wrong

Questions Not Attempted

Total Questions on Quiz

Question Details

Results

Date

Score

Hint

Time allowed

minutes

seconds

Time used

Answer Choice(s) Selected

Question Text

All done

Need more practice!

Keep trying!

Not bad!

Good work!

Perfect!

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.

In the question about the equation for the line through A and B, your TeX isn’t rendering properly.

The question about the acute angle between l1 and l2, I think the answer should be none of these since the lines don’t intersect. Then the next question asks about their intersection point and I still think they don’t intersect! Maybe I’m making a huge mistake here. I get $\lambda = -2$ and $\mu = 1$ to make the $x$ and $y$ coordinates match, but then I get $-4$ and $-6$ for the $z$ coordinate.

Also you shouldn’t say “the equation”, you should say “an equation”.

## MathbloggingAll

C4 Vectors quiz http://t.co/9bpTtnvZWr

## Joshua Zucker

In the question about the equation for the line through A and B, your TeX isn’t rendering properly.

The question about the acute angle between l1 and l2, I think the answer should be none of these since the lines don’t intersect. Then the next question asks about their intersection point and I still think they don’t intersect! Maybe I’m making a huge mistake here. I get $\lambda = -2$ and $\mu = 1$ to make the $x$ and $y$ coordinates match, but then I get $-4$ and $-6$ for the $z$ coordinate.

Also you shouldn’t say “the equation”, you should say “an equation”.