Question

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

• A. $0.1$
• B. $\sqrt{0.11}$
• C. $\sqrt{0.8}$
• D. $1$

Answer 1

The correct option is B

$\sqrt{0.11}$

Explanation for the correct option

Given unit vector is $0.5\hat{i}+0.8\hat{j}+c\hat{k}$

The magnitude of a vector $\overrightarrow{a}$ is given as,
$\left|\overrightarrow{a}\right|=\sqrt{{a_1}^2+{a_2}^2+{a_3}^3}$
Where $a_1$, $a_2$, and $a_3$ are the coefficients of the direction vectors along the three axes.

Here, $a_1=0.5$, $a_2=0.8$ and $a_3=c$

We also know that, the magnitude of a unit vector is $1$. Thus,
$\begin{array}{cc}& \sqrt{{\left(0.5\right)}^2+{\left(0.8\right)}^2+c^2}=1\\ \Rightarrow & 0.25+0.64+c^2=1\\ \Rightarrow & c^2=0.11\\ \therefore & c=\sqrt{0.11}\end{array}$

Hence, option(B) i.e. $\sqrt{0.11}$ is correct.