COMEDK · Maths · 33. Vector Algebra
If \((\vec{a} + \vec{b}) \perp \vec{b}\) and \((\vec{a} + 2\vec{b}) \perp \vec{a}\), then
- A \(|\vec{a}| = \sqrt{2}|\vec{b}|\)
- B \(|\vec{a}| = 2|\vec{b}|\)
- C \(2|\vec{a}| = |\vec{b}|\)
- D \(|\vec{a}| = |\vec{b}|\)
Answer & Solution
Correct Answer
(A) \(|\vec{a}| = \sqrt{2}|\vec{b}|\)
Step-by-step Solution
Detailed explanation
Given \((\vec{a} + \vec{b}) \perp \vec{b}\), taking the dot product with \(\vec{b}\) gives zero: \((\vec{a} + \vec{b}) \cdot \vec{b} = 0\) \(\vec{a} \cdot \vec{b} + |\vec{b}|^2 = 0\) \(\vec{a} \cdot \vec{b} = -|\vec{b}|^2\) Also given \((\vec{a} + 2\vec{b}) \perp \vec{a}\),…
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