Three Dimensional Geometry Question 349
Question: The points (4, 7, 8), (2, 3, 4), (-1, -2, 1) and (1, 2, 5) are the vertices of a
Options:
A) Parallelogram
B) Rhombus
C) Rectangle
D) Square
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let the points are A, B, C and D respectively Mid-point of AC is $ ( \frac{4-1}{2},\frac{7-2}{2},\frac{8+1}{2} ) $ or $ ( \frac{3}{2},\frac{5}{2},\frac{9}{2} ) $ . Mid point of BD is $ ( \frac{2+1}{2},\frac{3+2}{2},\frac{4+5}{2} ) $ or $ ( \frac{3}{2},\frac{5}{2},\frac{9}{2} ) $ . Thus AC and BD bisect each other. Further, $ AC=\sqrt{{{(4+1)}^{2}}+{{(7+2)}^{2}}+{{(8-1)}^{2}}} $ $ =\sqrt{25+81+49}=\sqrt{155} $ $ BD=\sqrt{{{(2-1)}^{2}}+{{(3-2)}^{2}}+{{(4-5)}^{2}}} $ $ =\sqrt{1+1+1}=\sqrt{3} $
$ \therefore AC\ne BD $ . Hence, ABCD represents a parallelogram.
BETA
