ID: Class: 12 Subject: Math Topic: Vector Algebra Type: Very short (VSA) Year: 2024

Question:

If \(\vec{a}\) and \(\vec{b}\) are two non-zero vectors such that \((\vec{a}+\vec{b})\perp\vec{a}\) and \((2\vec{a}+\vec{b})\perp\vec{b}\), then prove that \(|\vec{b}|=\sqrt{2}|\vec{a}|\).