2.1 – N – Vector Introduction – Exercise Problems

Part – A

\[1.\ If\ \overrightarrow{a}= 2\overrightarrow{i}\ + 3\overrightarrow{j} + \overrightarrow{k}\ and\ \overrightarrow{b}= 3\overrightarrow{i}\ – \overrightarrow{j} + \overrightarrow{k}\, find\ 2\overrightarrow{a}\ +\ 3\overrightarrow{b}\ \hspace{20cm}\]
\[2.\ If\ position\ vectors\ of\ the\ points\ A\ and\ B\ are\ 2\overrightarrow{i}\ -\overrightarrow{j} + 3\overrightarrow{k}\ and\ 5\overrightarrow{i}\ + \overrightarrow{j} – 2\overrightarrow{k}\ find\ \overrightarrow{|AB|}\ \hspace{20cm}\]
\[3.\ Find\ the\ unit\ vector\ along\ the\ vector\ 2\overrightarrow{i}\ – \overrightarrow{j}- \overrightarrow{k}\ \hspace{20cm}\]

Part –B

1. Show that the points whose position vectors

\[2\overrightarrow{i}\ – \overrightarrow{j} + 3\overrightarrow{k},\ 3\overrightarrow{i}\ – 5\overrightarrow{j} + \overrightarrow{k}\ and\ -\overrightarrow{i}\ +11 \overrightarrow{j}+ 9\overrightarrow{k}\ are\ collinear\ \hspace{10cm}\]

Part –C

  1. Prove that the points
\[2\overrightarrow{i}\ + 3\overrightarrow{j}+ 4\overrightarrow{k}, 3\overrightarrow{i}\ + 4\overrightarrow{j}+ 2\overrightarrow{k} and\ 4\overrightarrow{i}\ +2 \overrightarrow{j}+ 3\overrightarrow{k}\ form\ an\ equilateral\ triangle\]

2. Prove that the points whose position  vectors  are

\[2\overrightarrow{i}\ – \overrightarrow{j}+ \overrightarrow{k}, \overrightarrow{i}\ – 3\overrightarrow{j} – 5\overrightarrow{k} and\ 3\overrightarrow{i}\ -4 \overrightarrow{j} – 4\overrightarrow{k}\ form\ a\ right\ angled\ triangle\]

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