Question

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ then the value of 'c' is

• A. 1
• B. $\sqrt{0.8}$
• C. $\sqrt{0.11}$
• D. $\sqrt{0.01}$

Answer 1

The correct option is C $\sqrt{0.11}$

$\text{Step 1: Finding the value of c}$

Given: $\hat{A}=0.5\hat{i}+0.8\hat{j}+c\hat{k}$

Magnitude of a unit vector is always $1$

$\therefore |\hat{A}|=1$

$\Rightarrow$ $\sqrt{{0.5}^2+{0.8}^2+c^2}=1$

$\Rightarrow$ $c^2=0.11$

$\Rightarrow$ $c=\sqrt{0.11}$

Hence option $C$ is correct.