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NDA 2019 Maths · Mathematics · Three Dimensional Geometry · easy

If θ is the acute angle between the planes x+2y+2z=5 and 4x-3z=2, then cos θ equals

Single correct option

If θ\theta is the acute angle between the planes x+2y+2z=5x+2y+2z=5 and 4x−3z=24x-3z=2, then cos⁡θ\cos\theta equals
  1. A. 1415\frac{14}{15}
  2. B. 25\frac25
  3. C. 215\frac2{15}
  4. D. 13\frac13
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Answer: (C) 215\frac2{15}

The angle between planes equals the angle between their normals (1,2,2)(1,2,2) and (4,0,−3)(4,0,-3). The dot product is 4−6=−24-6=-2, and the magnitudes are 33 and 55. So cos⁡θ=∣−2∣15=215\cos\theta=\frac{|-2|}{15}=\frac2{15} (acute angle needs the absolute value). Forgetting the modulus gives a negative value, which is not an acute angle.
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Original question written in the NDA 2019 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