Question

The vector $\overline{a}=1/7(2\overline{i}+3\overline{j}+6\overline{k})$
$\overline{b}=\frac{1}{7}(3\overline{i}-6\overline{j}+2\overline{k})\overline{c}=\frac{1}{7}(6i+2j-3k)$

• A. a right handed system
• B. an orthogonal system
• C. a left handed system
• D. on orthonormal system

Answer 1

Answer: (A), (B)

The correct options are
A a right handed system
B an orthogonal system

$\overrightarrow{a}=\frac{1}{7}(2\overrightarrow{i}+3\overrightarrow{j}+6\overrightarrow{k})$

$\overrightarrow{b}=\frac{1}{7}(3\overrightarrow{i}-6\overrightarrow{j}+2\hat{k})$

$\overrightarrow{c}=\frac{1}{7}(6\overrightarrow{i}-2\overrightarrow{j}-3\overrightarrow{k})$

$\overrightarrow{a}\cdot \overrightarrow{b}=\frac{1}{49}(6-18+12)=0$

$\overrightarrow{b}\cdot \overrightarrow{c}=\frac{1}{49}(18-12-6)=0$

$\overrightarrow{c}\cdot \overrightarrow{a}=\frac{1}{49}(12+6-18)=0$

Also $|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=1$

Hence $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ form an orthonormal system.

Also, we get $\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}$

$\overrightarrow{b}\times \overrightarrow{c}=\overrightarrow{a}$

and $\overrightarrow{c}\times \overrightarrow{a}=\overrightarrow{b}$

These vectors as well as form a right handed system.