Question

Find the lengths of the following vectors :
$3\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$, $\sqrt{2}i-\sqrt{3}k$, $5\overrightarrow{i}+4\overrightarrow{j}-2\overrightarrow{k}$

• A. $\sqrt{14},\sqrt{5},\sqrt{45}$
• B. $4,\sqrt[2]{22}+\sqrt[2]{23},7$
• C. $14,5,45$
• D. none of these

Answer 1

The correct option is A $\sqrt{14},\sqrt{5},\sqrt{45}$

For $3\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$
Length $=\sqrt{{\left(3\right)}^2+{\left(2\right)}^2+{\left(1\right)}^2}$

$=\sqrt{9+4+1}$

$=\sqrt{14.}$
For $\sqrt{2}\overrightarrow{i}-\sqrt{3}\overrightarrow{k}$
Length $=\sqrt{{\left(\sqrt{2}\right)}^2+{\left(\sqrt{3}\right)}^3}$

$=\sqrt{2+3}$

$=\sqrt{5}$
For $5\overrightarrow{i}+4\overrightarrow{j}-2\overrightarrow{k}$:
Length $=\sqrt{{\left(5\right)}^2+{\left(4\right)}^2+{\left(2\right)}^2}$

$=\sqrt{25+16+4}$

$=\sqrt{45}$