Q125 / 160 · TS EAMCET 2020 (10 Sep Shift 1) · Physics
If $0.5 \hat{\mathbf{i}}+0.8 \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is a unit vector, then $c$ is
- A$\sqrt{0.89}$
- B0.2
- C0.3
- Correct answerD$\sqrt{0.11}$
Solution
$\begin{array}{r}\text { Given, unit vector is } 0.5 \hat{\mathbf{i}}+0.8 \hat{\mathbf{j}}+c \hat{\mathbf{k}} \\ =\frac{1}{2} \hat{\mathbf{i}}+\frac{4}{5} \hat{\mathbf{j}}+c \hat{\mathbf{k}}\end{array}$
$\begin{aligned} & \Rightarrow \quad \sqrt{\left(\frac{1}{2}\right)^2+\left(\frac{4}{5}\right)^2+c^2}=1 \\ & \Rightarrow \quad \frac{1}{4}+\frac{16}{25}+c^2=1 \Rightarrow c^2=\frac{11}{100} \Rightarrow c=\sqrt{0.11}\end{aligned}$
Hence, the correct answer is option: 'D'.