Question

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

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

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

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

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

Find the area of the parallelogram whose diagonals are represented by the vectors $\stackrel{\rightarrow}{a}\$ = $2{\hat{i}}-3{\hat{j}}+4{\hat{k}}$ and ${\vec{b}}=2{\hat{i}}-{\hat{j}}+2{\hat{k}}$