Question

If $0.5\hat{i}+0.8\hat{j}+C\hat{k}$ is a unit vector then $C$ is

• A. $\sqrt{0.89}$
• B. $0.2$
• C. $0.3$
• D. $\sqrt{0.11}$

Answer 1

Answer: (D)

Given, unit vector is $0.5\hat{i}+0.8\hat{j}+c\hat{k}$
$=\frac{1}{2}\hat{i}+\frac{4}{5}\hat{j}+c\hat{k}$
$\Rightarrow \sqrt{{\left(\frac{1}{2}\right)}^2+{\left(\frac{4}{5}\right)}^2+c^2}=1$
$\Rightarrow \frac{1}{4}+\frac{16}{25}+c^2=1$
$\Rightarrow c^2=\frac{11}{100}$
$\Rightarrow c=\sqrt{0.11}$