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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

Find \(x\), \(y\) and \(z\) if \(\left( {\begin{array}{*{20}{c}}

{x – 3}\\

{y + 2}\\

{z + 4}

\end{array}} \right) = \left( {\begin{array}{*{20}{c}}

1\\

3\\

{ – 2}

\end{array}} \right)\)\(x = \) , \(y = \) , \(z = \)

CorrectIncorrect - Question 2 of 10
##### 2. Question

Find scalars \(a\), \(b\) and \(c\), if \(2\left( {\begin{array}{*{20}{c}}

1\\

2\\

{c + 1}

\end{array}} \right) = \left( {\begin{array}{*{20}{c}}

{a – 1}\\

b\\

6

\end{array}} \right)\).\(a = \) , \(b = \) , \(c = \)

CorrectIncorrect - Question 3 of 10
##### 3. Question

Find \(k\), correcting to two significant figures, such a vector \(k\left( {\begin{array}{*{20}{c}}

2\\

{ – 3}\\

2

\end{array}} \right)\) is in the same direction as \(\left( {\begin{array}{*{20}{c}}

2\\

{ – 3}\\

2

\end{array}} \right)\) and with length 4 units.CorrectIncorrect - Question 4 of 10
##### 4. Question

Find \(\vec a \bullet \vec b\) if \(\left| {\vec a} \right| = 2,\left| {\vec b} \right| = 4,\theta = 130^\circ \), correcting to two significant figures.

CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\vec a \bullet \vec b}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)

- Question 5 of 10
##### 5. Question

Find \(k\) given \(\vec a = \left( {\begin{array}{*{20}{c}}

2\\

k

\end{array}} \right)\) and \(\vec b = \left( {\begin{array}{*{20}{c}}

5\\

1

\end{array}} \right)\) are perpendicular.CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\vec a \bullet \vec b}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)

- Question 6 of 10
##### 6. Question

Find a line parallel to \( – \vec i + 4\vec j\) which cuts the \(x\)-axis at 3 using a Cartesian equation.

CorrectIncorrect - Question 7 of 10
##### 7. Question

Find the coordinates \(\left( {a,b,c} \right)\) of the point where the line with parametric equations \(x = – 2 + 2t,{\rm{ }}y = – 3 – 3t\) and \(z = -4 + 2t\) meets the \(YOZ\) plane.

\(a = \) , \(b = \) , \(c = \)

CorrectIncorrect - Question 8 of 10
##### 8. Question

Find the acute angle, correcting to the nearest degree, between the lines: \(x + 2y = 4\) and \(2x – y = 3\).

degree(s)

CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\left| {\vec a \bullet \vec b} \right|}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)

- Question 9 of 10
##### 9. Question

Find the acute angle, correcting to the nearest degree, between the lines: \(x + 2y = 4\) and \(x = – 2y + 3\).

degree(s)

CorrectIncorrect##### Hint

\(\cos \theta = \dfrac{{\left| {\vec a \bullet \vec b} \right|}}{{\left| {\vec a} \right|\left| {\vec b} \right|}}\)

- Question 10 of 10
##### 10. Question

A line has a vector equation \(\left( {\begin{array}{*{20}{c}}

x\\

y

\end{array}} \right) = \left( {\begin{array}{*{20}{c}}

3\\

6

\end{array}} \right) + t\left( {\begin{array}{*{20}{c}}

5\\

{ – 4}

\end{array}} \right)\). Find the shortest distance from \(P\left( {2,3} \right)\) to the line, correcting to three significant figures.CorrectIncorrect