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11. three dimension geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths11. three dimension geometry1 Mark
MCQ
The triangle formed by the points $(0, 7, 10), (-1, 6, 6), (-4, 9, 6)$ is
  • A
    Equilateral
  • B
    Isosceles
  • C
    Right angled
  • ✓
    Right angled Isosceles
✓

Answer

Correct option: D.
Right angled Isosceles
d
(d) Let $A$ be $(0, 7, 10), B\ (-1, 6, 6)$ and $C\ (-4, 9, 6)$

Then, $AB = \sqrt {1 + 1 + 16} = \sqrt {18} = 3\sqrt 2 $

$BC = \sqrt {9 + 9 + 0} = \sqrt {18} = 3\sqrt 2 $

$AC = \sqrt {16 + 4 + 16} = \sqrt {36} = 6$

Clearly, $A{C^2} = A{B^2} + B{C^2}$

Hence $\Delta $ is right angled. Also, since $AB = BC$

 $\Delta $ is right angled isosceles.

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