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 vector in the direction of vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$which has magnitude 21 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 unit vector in the direction of $\stackrel{\rightarrow}{A}$ = $3\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).

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

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