First slide

Introduction to 3-D Geometry

Question

The points $P (1, 3, 4), Q (- 1, 6, 10), R (- 7, 4, 7)$ and $S$ forms Rhombus then $S =$

Easy

A

$(1, 1, 5)$
B

$(- 5, 1, 1)$
C

$(2, 4, 5)$
D

$(2, 4, - 5)$

Solution

The points $P (1, 3, 4), Q (- 1, 6, 10), R (- 7, 4, 7)$ forms Rhombus in the order.
The fourth vertex is $S = P + R - Q$
Hence, $S = (1 - 7 + 1, 3 + 4 - 6, 4 + 7 - 10) = (- 5, 1, 1)$
Therefore, the fourth vertex is $(- 5, 1, 1)$

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