Question

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

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 angle between the vectors ${\vec{a}}={\hat{i}}+{\hat{j}}-{\hat{k}}$ and ${\vec{b}}={\hat{i}}-{\hat{j}}+{\hat{k}}$

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

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 a line has direction ratios 2, – 1, – 2, then what are its direction cosines ?

Write the projection of the vector $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ along the vector $\stackrel{\rightarrow}{j}\$.