Question

$0.4\stackrel{⏜}{i}+0.8\stackrel{⏜}{j}+c\hat{k}$ represents a unit vector when $c$ is

• A. $-0.2$
• B. $\sqrt{0.2}$
• C. $\sqrt{0.8}$
• D. $0$

Answer 1

The correct option is B

$\sqrt{0.2}$

Explanation for the correct option:

Given vector $0.4\stackrel{⏜}{i}+0.8\stackrel{⏜}{j}+c\hat{k}$ is a unit vector so its magnitude should be $1$

So, $\sqrt{{\left(0.4\right)}^2+{\left(0.8\right)}^2+c^2}=1$

$\Rightarrow 0.16+0.64+c^2=1$

$\Rightarrow 0.8+c^2=1$

$\Rightarrow c^2=0.2$

$\Rightarrow c=\pm \sqrt{0.2}$

Hence, Option ‘B’ is Correct.