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

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.

Find the vector equation of the following diagram.

Find  \(\overrightarrow {BM} \).

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

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

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.

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

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.

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.