If \(\vec a\) and \(\vec b\) are two non-zero orthogonal vectors, then \(|\vec a + \vec b|\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(|\vec a-\vec b|\)
Orthogonal vectors have \(\vec a \cdot \vec b = 0\). Expanding the squares of the magnitudes:
\(|\vec a + \vec b|^2 = |\vec a|^2 + 2\,\vec a \cdot \vec b + |\vec b|^2 = |\vec a|^2 + |\vec b|^2\)
\(|\vec a - \vec b|^2 = |\vec a|^2 - 2\,\vec a \cdot \vec b + |\vec b|^2 = |\vec a|^2 + |\vec b|^2\)
The squares are equal and magnitudes are non-negative, so \(|\vec a + \vec b| = |\vec a - \vec b|\). Geometrically, these are the two diagonals of a rectangle with sides \(\vec a\) and \(\vec b\).