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  • The length of the perpendicular from the point   on the line passing through  <img alt="(1,2,4)" src="/latex-imag

The length of the perpendicular from the point (1,-2,5)  on the line passing through  (1,2,4)  and parallel to the line \mathrm{x+y-z=0=x-2 y+3 z-5} is:

Option: 1

\sqrt{\frac{21}{2}}


Option: 2

\sqrt{\frac{9}{2}}


Option: 3

\sqrt{\frac{73}{2}}


Option: 4

1


Answers (1)

best_answer

d.r's of the line  \mathrm{=\left|\begin{array}{ccc} \hat{i} \cdot &\hat{J} & \hat{k} \\ 1 & 1 & -1 \\ 1 & -2 & 3 \end{array}\right|=\hat{i}-4 \hat{J}-3 \hat{k}}

Equation of line is  \mathrm{\overrightarrow{r}=\hat{i}+2 \hat{j}+4 \hat{k}+\lambda(\hat{i}-4 \hat{J}-3 \hat{k})} \\

\mathrm{\text { Let } A(1,2,4) \text { and } P \text { be }(1+\lambda, 2-4 \lambda, 4-3 \lambda)} \\

\mathrm{\therefore \overrightarrow{P A} \cdot(\hat{i}-4 \hat{j}-3 \hat{k})=0} \\

\mathrm{\lambda=\frac{1}{2} . P\left(\frac{1}{2}, 2,-\frac{5}{2}\right)} \\

\mathrm{|A P|=\sqrt{\frac{21}{2}}}

Hence correct option is 1

Posted by

HARSH KANKARIA

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