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 $
$\Rightarrow c^{2}=\frac{11}{100}$
$\Rightarrow c=\sqrt{0.11}$