Question

If the points $P(2,1,-3),Q(5,4,3)$ and $R(1,4,7)$ are three vertices of a parallelogram $PQRS$ then the other vertex is

• A. $(1,0,0)$
• B. $(-2,1,1)$
• C. $(-2,2,1)$
• D. $(2,1,2)$

Answer 1

The correct option is B $(-2,1,1)$

Mid point of $PR$ is $(\frac{2+1}{2},\frac{1+4}{2},\frac{-3+7}{2})=(\frac{3}{2},\frac{5}{2},2)$

Let the other point be $S(a,b,c)$

Mid point of $QS$ is $(\frac{5+a}{2},\frac{4+b}{2},\frac{3+c}{2})$

In parallelogram $PQRS$

Mid point of diagnols coincides

$⟹5+a=3,4+b=5,3+c=4⟹a=-2,b=1,c=1$

$S(-2,1,1)$