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) → \(\sqrt{3}\)
For unit vectors, \(|\vec a| = |\vec b| = |\vec c| = 1\). Being mutually perpendicular, \(\vec a \cdot \vec b = \vec b \cdot \vec c = \vec c \cdot \vec a = 0\).
\(|\vec a + \vec b + \vec c|^2 = |\vec a|^2 + |\vec b|^2 + |\vec c|^2 + 2(\vec a \cdot \vec b + \vec b \cdot \vec c + \vec c \cdot \vec a)\)
\(= 1 + 1 + 1 + 0 = 3\)
\(|\vec a + \vec b + \vec c| = \sqrt{3}\)