ASSIGNMENT – I FOR ENGINEERING MATHEMATICS – II

\[\LARGE {\color {red}{Questions\ from\ Unit-I\ and\ Unit-II}}\]
\[Date:\ 09-04-2022\ \hspace{10cm}\ Max\ Marks:\ 4\ ×\ 5\ =\ 20m\]
\[1.\ Show\ that\ the\ circles\ x^2 + y^2 – 4x + 6y – 8 = 0\ and\ \hspace{10cm}\]\[x^2 + y^2 – 10x – 6y +\ 14\ =\ 0\ touch\ each\ other.\ \hspace{10cm}\]
\[2.\ Find\ ‘α’ \ such\ that\ the\ equation\ \ 3\ x^2\ +\ 7\ x\ y\ +\ α\ y^2\ -\ 4\ x\ -\ 13\ y\ -\ 7\ =\ 0\ \hspace{7cm}\]\[represents\ a\ pair\ of\ straight\ lines\ \hspace{5cm}\]
\[3.\ The\ position\ vectors\ of\ the\ \triangle\ ABC\ are\ \hspace{18cm}\]\[2\overrightarrow{i}\ – \overrightarrow{j}+ \overrightarrow{k}, \overrightarrow{i}\ – 3\overrightarrow{j} – 5\overrightarrow{k} and\ 3\overrightarrow{i}\ -4 \overrightarrow{j} – 4\overrightarrow{k}\ respectively.\ Prove\ that\ triangle\ is\ right\ angled\ \hspace{10cm}\]
\[4.\ Find\ the\ unit\ vector\ perpendicular\ to\ each\ of\ the\ vectors\ 3\overrightarrow{i}\ -\ 3\overrightarrow{j}\ +\ 2\overrightarrow{k} and\ 4\overrightarrow{i}\ -\ 2\overrightarrow{j}\ +\ \overrightarrow{k}.\ \hspace{10cm}\]\[Also\ find\ the\ sine\ of\ the\ angle\ between\ the\ vectors .\ \hspace{10cm}\]