Let the image of the point P(1, 2, 3) in the line $L:\frac{x-6}{3}=\frac{y-1}{2}=\frac{z-2}{3}$  be Q $LetR\left(\alpha ,\beta ,\gamma \right)$ .  be a point that divides internally the line segment PQ in the ration 1 : 3. Then the value of $22\left(\alpha +\beta +\gamma \right)$  is equal to………….

Any point on line L is

M (3r + 6, 2r + 1, 3r + 2)                                                          

$\overrightarrow{PM}\perp rtoL$          

$\therefore 3\left(3r+5\right)+2\left(2r-1\right)+3\left(3r-1\right)=0$          

$r=\frac{-5}{11}$

 

<p>Any point on line L is</p><p>M (3r + 6, 2r + 1, 3r + 2)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mover accent="true"> <mrow> <mi>P</mi> <mi>M</mi> </mrow> <mo stretchy="true">→</mo> </mover> <mo>⊥</mo> <mi>r</mi> <mtext> </mtext> <mtext> </mtext> <mi>t</mi> <mi>o</mi> <mtext> </mtext> <mtext> </mtext> <mi>L</mi> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mo>∴</mo> <mn>3</mn> <mrow> <mo> (</mo> <mrow> <mn>3</mn> <mi>r</mi> <mo>+</mo> <mn>5</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <mrow> <mo> (</mo> <mrow> <mn>2</mn> <mi>r</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>3</mn> <mrow> <mo> (</mo> <mrow> <mn>3</mn> <mi>r</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mi>r</mi> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mn>5</mn> </mrow> <mrow> <mn>1</mn> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753185711phpfmJ0s8.jpeg" alt="" width="490" height="325" loading="lazy"></picture></div></div><p>&nbsp;</p>

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