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NDA 2018 Maths · Mathematics · Vector Algebra · medium

The triangle with vertices P(1,2,3), Q(4,2,3) and R(1,6,3) is

Single correct option

The triangle with vertices P(1,2,3)P(1,2,3), Q(4,2,3)Q(4,2,3) and R(1,6,3)R(1,6,3) is
  1. A. equilateral
  2. B. isosceles but not right-angled
  3. C. right-angled
  4. D. obtuse-angled
Show answer and solution

Answer: (C) right-angled

PQ⃗=(3,0,0)\vec{PQ}=(3,0,0) and PR⃗=(0,4,0)\vec{PR}=(0,4,0), so PQ⃗⋅PR⃗=0\vec{PQ}\cdot\vec{PR}=0 and the angle at PP is 90∘90^\circ. The sides are 33, 44 and QR=9+16=5QR=\sqrt{9+16}=5, a Pythagorean triple, so it is not isosceles either.
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Original question written in the NDA 2018 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