Consider points A(0,0,0), B(1,1,1) and plane P : x − y + z = 3 . Let Q ( a , b , c ) be a moving point on plane P then identify the correct statement(s)

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For (QA + QB) min, Q must lie on AB' line where B' is mirror image of B in plane $x - y + z = 3$

$B^{'} \equiv (\frac{7}{3}, \frac{- 1}{3}, \frac{7}{3})$

Q is intersection of AB' and plane

$Q (\frac{7}{5}, \frac{- 1}{5}, \frac{7}{5}) \equiv (a, b, c)$

Hence $a - c - 10 b = 2$ For $∣ QA - QB ∣_{min}, Q$ must lie on point of intersection of AB with plane

$Q \equiv (3, 3, 3) \equiv (a, b, c)$ Hence $a - 2 b + c = 0$

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