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NEET 2004
Exam
NEET
Year
2004
Subject
Physics
Chapter
Mathematics in Physics

NEET 2004 · Physics · Mathematics in Physics

If | A × B |= 3 A · B then the value of | A + B | is:

If ∣A⃗×B⃗∣=3A⃗⋅B⃗|\vec{A} \times \vec{B}|=\sqrt{3} \vec{A} \cdot \vec{B} then the value of ∣A⃗+B⃗∣|\vec{A} + \vec{B}| is:

Options

  1. A(A2+B2+AB)1/2\left(A^2+B^2+A B\right)^{1 / 2}
  2. B(A2+B2+AB3)1/2\left(A^2+B^2+\frac{A B}{\sqrt{3}}\right)^{1 / 2}
  3. CA+BA+B
  4. D(A2+B2+3AB)1/2\left(A^2+B^2+\sqrt{3} A B\right)^{1 / 2}

Correct answer

A. (A2+B2+AB)1/2\left(A^2+B^2+A B\right)^{1 / 2}

Step-by-step solution

According to the question A⃗×B⃗=3A⃗⋅B⃗ABsin⁡=3ABcos⁡θ⇒tan⁡θ=3⇒θ=60∘⇒∣A⃗+B⃗∣=∣A⃗∣2+∣B⃗∣2+2∣A∣B∣cos⁡θ‾\begin{aligned} & \vec{A} \times \vec{B}=\sqrt{3} \vec{A} \cdot \vec{B} \\ & A B \sin =\sqrt{3} A B \cos \theta \\ & \Rightarrow \tan \theta=\sqrt{3} \\ & \Rightarrow \theta=60^{\circ} \\ & \Rightarrow|\vec{A}+\vec{B}|=\sqrt{|\vec{A}|^2+|\vec{B}|^2+2|A|} \overline{B \mid \cos \theta} \end{aligned}
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