Question

The sine of the angle between the vectors $\overrightarrow{i}-2\overrightarrow{j}+3\overrightarrow{k}$ and $2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is

• A. $\frac{5}{2\sqrt{7}}$
• B. $\frac{5}{\sqrt{7}}$
• C. $\frac{3}{\sqrt{1}4}$
• D. $\frac{5}{21}$

Answer 1

Answer: (A)

$cos\theta =\frac{\vec{a}.\vec{b}}{|\vec{a}||\vec{b}|}$
$=\frac{2-2+3}{\sqrt{1+4+9}\sqrt{4+1+1}}$
$=\frac{3}{\sqrt{84}}=\frac{\sqrt{3}}{\sqrt{28}}$
$\therefore sin\theta =\sqrt{1-co{s}^2\theta }$
$=\sqrt{1-\frac{3}{28}}=\frac{5}{\sqrt{28}}=\frac{5}{2\sqrt{7}}$