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Question 1 of 10

1. Question

State the vectors which are equal to \(\vec x\).

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Question 2 of 10

2. Question

Consider the vector, \(\vec a\) , whose magnitude is 20 and whose true bearing is \(120^\circ \). Find \(x\) and \(y\) if \(\vec a = x\vec i + y\vec j\), correcting to two decimal places.

\(x = \) , \(y = \)

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Question 3 of 10

3. Question

Find the vector equation of the following diagram.

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Question 4 of 10

4. Question

Find \(\overrightarrow {BM} \).

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Question 5 of 10

5. Question

Find \(x\) and \(y\), if the vector \(\overrightarrow {BC} \) in unit vector form is \( x\vec{i} + y \vec{j} \)

\(x = \) , \(y = \)

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Question 6 of 10

6. Question

Find the positive value of \(k\), correcting to three significant figures, if the length of \( \begin{pmatrix} k \\ – 3 \end{pmatrix} \) is 7.2.

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Question 7 of 10

7. Question

Given \(\vec a = \left( {\begin{array}{*{20}{c}} 4\\ 5 \end{array}} \right)\) and \(\vec b = \left( {\begin{array}{*{20}{c}} { – 2}\\ 3 \end{array}} \right)\), find \(\left| {\vec a – \vec b} \right|\), correcting to two significant figures.

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Question 8 of 10

8. Question

Find \(k\) given the unit vector \(\left( {\begin{array}{*{20}{c}} {2k}\\ k\\ {0.2} \end{array}} \right)\), correcting to two significant figures.

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Question 9 of 10

9. Question

Given \(\vec a = \left( {\begin{array}{*{20}{c}} 3\\ 5\\ { – 1} \end{array}} \right),\vec b = \left( {\begin{array}{*{20}{c}} 1\\ 3\\ { – 4} \end{array}} \right)\) and \(\vec c = \left( {\begin{array}{*{20}{c}} 3\\ – 2\\ 7 \end{array}} \right)\), find \(\left| {\vec a – \vec b + 3\vec c} \right|\), correcting to two significant figures.

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Question 10 of 10

10. Question

Find \(k\), correcting to two significant figures, such a vector \(k\left( {\begin{array}{*{20}{c}} 4\\ { – 5}\\ 2 \end{array}} \right)\) is in the opposite direction as \(\left( {\begin{array}{*{20}{c}} 4\\ { – 5}\\ 2 \end{array}} \right)\) and with length 3 units.