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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Vector Algebra

NDA 2010 · Mathematics · Vector Algebra

If the angle between the vector a and b is (π)/(3) , what is the...

If the angle between the vector a⃗\vec{a} and b⃗\vec{b} is π3\frac{\pi}{3}, what is the angle between −5a⃗-5 \vec{a} and 6b⃗6 \vec{b} ?

Options

  1. Aπ6\frac{\pi}{6}
  2. B2π3\frac{2 \pi}{3}
  3. C2π5\frac{2 \pi}{5}
  4. D3π7\frac{3 \pi}{7}

Correct answer

B. 2π3\frac{2 \pi}{3}

Step-by-step solution

cos⁡θ=a⃗b⃗∣a⃗∥b⃗∣cos⁡θ=.5a⃗⋅6b⃗.5×6=−a⃗⋅b⃗∣a⃗∣∣b⃗∣=cos⁡(π−π3)=2π/3.\begin{aligned} & \cos \theta=\frac{\vec{a} \vec{b}}{|\vec{a} \| \vec{b}|} \\ & \cos \theta=\frac{.5 \vec{a} \cdot 6 \vec{b}}{.5 \times 6}=\frac{-\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|} \\ & =\cos \left(\pi-\frac{\pi}{3}\right)=2 \pi / 3.\end{aligned}
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