Question

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ , then the value of $\text{‘}{c}^{\prime }$ is

• A. $1$
• B. $\sqrt{0.11}$
• C. $\sqrt{0.01}$
• D. $\sqrt{0.39}$

Answer 1

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

Magnitude of a unit vector =$1$
$\therefore$ Putting the values of coefficients of given unit vector in the formula,
$\sqrt{{A_x}^2+{A_y}^2+{A_z}^2}=1$
$\Rightarrow \sqrt{(0.5{)}^2+(0.8{)}^2+c^2}=1\Rightarrow c=\sqrt{0.11}$
Hence option B is correct.