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
$(-1, 3.5, 0.5)$
B
$(3, 0.5, 3.5)$
C
$(5,-1,5)$
D
$(2,3,0)$
E
There is no such point.
Question 2
Point $A$ is at $\begin{pmatrix} 9\\ 0 \\ 3 \\ \end{pmatrix}$ and point $B$ is at $\begin{pmatrix} -3\\ 8 \\ -3 \\ \end{pmatrix}$. What is the distance $AB$?
A
$244$
B
$26$
C
$71$
D
$109$
E
$\sqrt{244}$
Question 3
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
$\begin{pmatrix}
12\\ -8 \\ 6 \\
\end{pmatrix}$
B
71º
C
109º
D
$\begin{pmatrix}
-12 \\ 8 \\ -6 \\
\end{pmatrix}$
E
$\sqrt{244}$
Question 4
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
$\begin{pmatrix}5\\-1\\5\end{pmatrix}$
B
$\begin{pmatrix}17\\-2\\8\end{pmatrix}$
C
$\begin{pmatrix}1\\2\\2\end{pmatrix}$
D
$\begin{pmatrix}-7\\8\\-4\end{pmatrix}$
E
You can't fool me, they don't!
Question 5
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
137º
B
None of these
C
43º
D
167º
E
13º
Question 6
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 $B$?
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”.