Q.1 (ii) If θ is the angle between two vectors bar a and bar b and |bar a·bar b|=|bar a×bar b| then θ is equal to ____. A. 0 B. π/4 or 3π/4 C. π/2 D. π or π/6

Answer: B. π/4 or 3π/4 Answer: (b) π/4 or 3π/4 |bar a·bar b|=|bar a||bar b||cosθ| and |bar a×bar b|=|bar a||bar b|sinθ . Equating, |cosθ|=sinθ , i.e. |tanθ|=1 . For 0≤θ≤π this gives θ=π/4 or 3π/4 .

Chapter: Vectors· Mathematics & Statistics Part 1

If \(\theta\) is the angle between two vectors \(\bar a\) and \(\bar b\) and \(|\bar a\cdot\bar b|=|\bar a\times\bar b|\) then \(\theta\) is equal to ____.

Q.1 (ii) If \(\theta\) is the angle between two vectors \(\bar a\) and \(\bar b\) and \(|\bar a\cdot\bar b|=|\bar a\times\bar b|\) then \(\theta\) is equal to ____.

A. 0

B. \(\dfrac{\pi}{4}\) or \(\dfrac{3\pi}{4}\)

C. \(\dfrac{\pi}{2}\)

D. \(\pi\) or \(\dfrac{\pi}{6}\)

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: B. \(\dfrac{\pi}{4}\) or \(\dfrac{3\pi}{4}\)

Answer: (b) \(\dfrac{\pi}{4}\) or \(\dfrac{3\pi}{4}\)

\(|\bar a\cdot\bar b|=|\bar a||\bar b||\cos\theta|\) and \(|\bar a\times\bar b|=|\bar a||\bar b|\sin\theta\). Equating, \(|\cos\theta|=\sin\theta\), i.e. \(|\tan\theta|=1\). For \(0\le\theta\le\pi\) this gives \(\theta=\dfrac{\pi}{4}\) or \(\dfrac{3\pi}{4}\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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If \(\theta\) is the angle between two vectors \(\bar a\) and \(\bar b\) and \(|\bar a\cdot\bar b|=|\bar a\times\bar b|\) then \(\theta\) is equal to ____.

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