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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

If the magnitude of a × b equals to a · b , then which one of the...

If the magnitude of a⃗×b⃗\vec{a} \times \vec{b} equals to a⃗⋅b⃗\vec{a} \cdot \vec{b}, then which one of the following is correct?

Options

  1. Aa⃗=b⃗\vec{a}=\vec{b}
  2. BThe angle between a⃗\vec{a} and b⃗\vec{b} is 45∘45^{{}^{\circ}}
  3. Ca⃗\vec{a} is parallel to b⃗\vec{b}
  4. Da⃗\vec{a} is perpendicular to b⃗\vec{b}

Correct answer

B. The angle between a⃗\vec{a} and b⃗\vec{b} is 45∘45^{{}^{\circ}}

Step-by-step solution

∣a⃗×b⃗∣=∣a⃗⋅b⃗∣∣a⃗∣∣b⃗∣sin⁡θ=∣a⃗∣∣b⃗∣cos⁡θtan⁡θ=1⇒θ=π4\begin{aligned} & |\vec{a} \times \vec{b}|=|\vec{a} \cdot \vec{b}| \\ & |\vec{a}||\vec{b}| \sin \theta=|\vec{a}||\vec{b}| \cos \theta \\ & \tan \theta=1 \quad \Rightarrow \theta=\frac{\pi}{4}\end{aligned}
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