Find a vector in the direction of $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\;\stackrel{\wedge}{j}$ that has magnitude 7 units.

Write a vector in the direction of the vector $\displaystyle{\hat{\iota}}-2\,{\hat{\iota}}+2\,{\hat{\iota}}$ that has magnitude 9 units.

Write a unit vector in the direction of the sum of vectors ${\vec{a}}{=}2\,\vec{i}+2\,\vec{j}-5\,\vec{k}\ \mathrm{~and}\ \vec{b}=2\,\vec{i}+\vec{j}-{7}\vec{k}.$

Find a vector in the direction of vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$which has magnitude 21 units.

If $\begin{array}{l l}{{\vec{a}=x\,\hat{i}+2\,\hat{j}-z\,\hat{k}~}}&{{\mathrm{and}~~~~\vec{b}=3\,\hat{i}-y\,\hat{j}+\hat{k}}}\end{array}$ are two equal vectors, then write the value of x + y + z.

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$

Find a unit vector parallel to the sum of vectors $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +5\stackrel{\wedge}{k}$

Find a unit vector in the direction of $\stackrel{\rightarrow}{A}$ = $3\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$

Find the sum of the vectors $\stackrel{\rightarrow}{a}=\hat{i}-2\hat{j}+\hat{k}\;,$ $\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}$ and $\stackrel{\rightarrow}{c}=\hat{i}-6\hat{j}-7\hat{k}.$

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\stackrel{\wedge}{j},$ $\vec{b}=2\hat{i}-3\hat{j},$ $\vec{c}=2\hat{i}+3\hat{k},$

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\hat{i}-3\hat{k},$ ${\vec{b}}=2{\hat{j}}-{\hat{k}},$ $\stackrel{\rightarrow}{c}=2\hat{i}-3\hat{j}+2\hat{k}.$

Write the number of vectors of unit length perpendicular to both the vector $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{2i}+\stackrel{\wedge}{j}+\stackrel{\wedge}{2k}$ and ${\vec{b}}={\hat{j}}+{\hat{k}}\,.$

Find the position vector of a point which divides the join of points with position vectors $\;\stackrel{\rightarrow}{(a}-2\stackrel{\rightarrow}{b})$ and $\;\stackrel{\rightarrow}{(2a}+\stackrel{\rightarrow}{b})$ externally in the ratio 2 : 1.

The two vectors $:{\hat{j}}+{\hat{k}}$ and $3\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ represent the two sides AB and AC, respectively of $\Delta A B C.$ Find the length of the median through A.

Write the position vector of the point which divides the join of points with position vectors $3\stackrel{\rightarrow}{a}-2\stackrel{\rightarrow}{b}$ and $2\stackrel{\rightarrow}{a}+3\stackrel{\rightarrow}{b}$ in the ratio 2:1.