If $\vec a,\vec b,\vec c$ are three mutually perpendicular unit vectors, then $|\vec a + \vec b + \vec c|$ is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\sqrt{3}$
Given $\vec a,\vec b,\vec c$ are mutually perpendicular unit vectors
$|\vec a|=|\vec b|=|\vec c|=1$ and $\vec a\cdot\vec b=\vec b\cdot\vec c=\vec c\cdot\vec a=0$
$|\vec a+\vec b+\vec c|^2=(\vec a+\vec b+\vec c)\cdot(\vec a+\vec b+\vec c)$
$=|\vec a|^2+|\vec b|^2+|\vec c|^2$
$=1+1+1$
$=3$
$|\vec a+\vec b+\vec c|=\sqrt3$
The value of $|\vec a+\vec b+\vec c|$ is $\sqrt3$.