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NDA 2017 Maths · Mathematics · Vector Algebra · medium

The sine of the angle between vec a=hat i+2hat j+2hat k and vec b=3hat j+4hat k is

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The sine of the angle between a⃗=i^+2j^+2k^\vec a=\hat i+2\hat j+2\hat k and b⃗=3j^+4k^\vec b=3\hat j+4\hat k is
  1. A. 1415\frac{14}{15}
  2. B. 295\frac{\sqrt{29}}{5}
  3. C. 29225\frac{29}{225}
  4. D. 2915\frac{\sqrt{29}}{15}
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Answer: (D) 2915\frac{\sqrt{29}}{15}

a⃗×b⃗=(2,−4,3)\vec a\times\vec b=(2,-4,3) with magnitude 29\sqrt{29}, while ∣a⃗∣∣b⃗∣=3×5=15|\vec a||\vec b|=3\times5=15, so sin⁡θ=2915\sin\theta=\frac{\sqrt{29}}{15}. The value 1415\frac{14}{15} is cos⁡θ=a⃗⋅b⃗15\cos\theta=\frac{\vec a\cdot\vec b}{15}, and 29225\frac{29}{225} is sin⁡2θ\sin^2\theta.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake