Let a, b$\in$R. If the mirror image of the point P(a, 6, 9) with respect to the line

${{x - 3} \over 7} = {{y - 2} \over 5} = {{z - 1} \over { - 9}}$ is (20, b, $-$a$-$9), then | a + b |, is equal to :

Given, P(a, 6, 9)<br/><br/>Equation of line ${{x - 3} \over 7} = {{y - 2} \over 5} = {{z - 1} \over { - 9}}$<br/><br/>Image of point P with respect to line is point Q(20, b, $-$a $-$9)<br/><br/>Mid-point of P and Q = $\left( {{{a + 20} \over 2},{{6 + b} \over 2},{{ - a} \over 2}} \right)$<br/><br/>This point lies on line<br/><br/>$\therefore$ $${{{{a + 20} \over 2} - 3} \over 7} = {{{{6 + b} \over 2} - 2} \over 5} = {{{{ - a} \over 2} - 1} \over { - 9}}$$<br/><br/>$\Rightarrow {{a + 14} \over {14}} = {{b + 2} \over {10}} = {{a + 2} \over {18}}$<br/><br/>$\Rightarrow {{a + 14} \over {14}} = {{a + 2} \over {18}}$ and ${{b + 2} \over {10}} = {{a + 2} \over {18}}$<br/><br/>Solving, we get a = $-$ 56, b = $-$ 32<br/><br/>$\therefore$ $\left| {a + b} \right| = \left| { - 56 - 32} \right| = 88$