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The distance of the point  \left ( -1,9,-16 \right ) from the plane 2x + 3y -z = 5  measured parallel to the line \frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12} \mathrm{is}

Option: 1

31


Option: 2

13\sqrt{2}


Option: 3

20\sqrt{2}


Option: 4

26


Answers (1)

best_answer



\mathrm{L}_{\mathrm{AB}}: \quad \frac{x+1}{3}=\frac{\mathrm{y}-9}{-4}=\frac{z+16}{12}=\mathrm{t}

\!\!\!\!\!\!\!\!\!B : \quad(3 t-1,9-4 t, 12 t-16)\; lies\; on\; plane\\ \begin{aligned} &\;\;\;\;\;\;\;\;\;\; 2(3 t-1)+3(9-4 t)-(12 t-16)=5 \\ &\;\;\;\;\;\;\;\;\;\; -18 t-2+27+16=5 \\ &\;\;\;\;\;\;\;\;\;\; -18 t+25+16=5 \\ &\;\;\;\;\;\;\;\;\;\; -18 t=-36 \quad \Rightarrow t=2 \end{aligned}
\begin{array}{ll} \text { B : } & (5,1,8) \quad A:(-1,9,-16) \\ & 1(\mathrm{AB})=\sqrt{36+64+576}=\sqrt{676}=26 \end{array}

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Divya Prakash Singh

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