Question

$A=(2,3,0)$ and $B=(2,1,2)$ are two points. If the points $P,Q$ are on the line $AB$ such that $AP=PQ=QB$, then $PQ=$

• A. $2\sqrt{2}$
• B. $6\sqrt{2}$
• C. $\sqrt{\frac{8}{9}}$
• D. $\sqrt{2}$

Answer 1

Answer: (C)

$\sqrt{\frac{8}{9}}$

$AB=\sqrt{(2-2{)}^2+(3-1{)}^2+(0-2{)}^2}=\sqrt{8}$

Since $AP=PQ=QB$

$\therefore PQ=\frac{AB}{3}=\frac{\sqrt{8}}{3}=\sqrt{\frac{8}{9}}$