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AP EAMCET · Maths · Three Dimensional Geometry

The points in the Argand plane represented by the complex numbers \(4 \overline{\mathrm{i}}+\overline{\mathrm{j}}+3 \overline{\mathrm{k}}\), \(6 \overline{\mathrm{i}}-2 \overline{\mathrm{j}}-3 \overline{\mathrm{k}}\) and \(\overline{\mathrm{i}}-\overline{\mathrm{j}}-3 \overline{\mathrm{k}}\) form

  1. A \(\text { a right - angled triangle }\)
  2. B \(\text { a right - angled isosceles triangle }\)
  3. C \(\text { an equilateral triangle }\)
  4. D \(\text { an isosceles triangle }\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\text { an isosceles triangle }\)

Step-by-step Solution

Detailed explanation

\(A = (4, 1), B = (6, -2), C = (1, -1)\) \(AB^2 = (6-4)^2 + (-2-1)^2 = 2^2 + (-3)^2 = 4+9 = 13\) \(BC^2 = (1-6)^2 + (-1-(-2))^2 = (-5)^2 + 1^2 = 25+1 = 26\) \(CA^2 = (4-1)^2 + (1-(-1))^2 = 3^2 + 2^2 = 9+4 = 13\) \(AB = \sqrt{13}, BC = \sqrt{26}, CA = \sqrt{13}\) Since…