Question

Given $\overrightarrow{A}=0.3\hat{i}+0.4\hat{j}+c\hat{k}$. Calculate the value of c if A is a unit vector.

• A. 0.75
• B. 0.87
• C. 0.96
• D. 0.45

Answer 1

The correct option is B

0.87

If $\overrightarrow{A}$ is a unit vector then its magnitude must be unity.
$\Rightarrow \sqrt{a_x^2+a_y^2+a_z^2}=1i.e.,\sqrt{(0.3{)}^2+(0.4{)}^2+c^2}=1$
or 0.09 + 0.16 + $c^2$ = 1
or $c^2$ = 1 - 0.25 = 0.75 or $c$ = 0.87