Three-Dimensional-Geometry Question 434
Question: The points (5, ? 4, 2), (4, ?3, 1), (7, ? 6, 4) and (8, ?7, 5) are the vertices of
[RPET 2002]
Options:
A) A rectangle
B) A square
C) A parallelogram
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ A(5,,-4,,2) $ , $ B(4,,-3,,1), $ $ C(7,,-6,,4) $ and $ D(8,,-7,,5) $ . Then $ AB=\sqrt{1+1+1}=\sqrt{3} $ , $ BC=\sqrt{9+9+9}=3\sqrt{3} $ , $ CD=\sqrt{1+1+1}=\sqrt{3} $ $ AD=\sqrt{9+9+9}=3\sqrt{3} $ . But $ \overrightarrow{AB},.,\overrightarrow{BC}\ne 0 $ Let the angle between AB and BC be $ \theta $ , then $ \cos \theta =-1\Rightarrow \theta =\pi $ . Hence option is correct.
BETA
