Question

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

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

Answer 1

Answer: (B)

$\sqrt{0.11}$

Given that:

$0.5\hat{i}+0.8\hat{j}+c\hat{k}=1$
$\sqrt{{0.5}^2+{0.8}^2+c^2}=1$

${0.5}^2+{0.8}^2+c^2=1$

$0.25+0.64+c^2=1$ or $c^2=1.0-0.89=0.11$

The magnitude of c is $\sqrt{0.11}$