Solve the following question:

Asked by joykphukan | 23rd Dec, 2015, 06:24: PM

Expert Answer:

bold Let bold space bold the bold space bold equation bold space bold of bold space bold a bold space bold plane bold space bold parallel bold space bold to bold space bold 4 bold x bold plus bold 12 bold y bold minus bold 3 bold z bold plus bold 1 bold equals bold 0 bold space bold and bold space bold passing bold space bold through bold space bold the bold space bold given bold space bold point bold space bold left parenthesis bold minus bold 2 bold comma bold space bold 3 bold comma bold space bold minus bold 4 bold right parenthesis bold space bold be bold 4 bold x bold plus bold 12 bold y bold minus bold 3 bold z bold plus bold d bold equals bold 0 bold Substituting bold space bold the bold space bold values bold space bold of bold space bold the bold space bold coordinates bold space bold in bold space bold the bold space bold equation bold comma bold space bold we bold space bold get bold 4 bold left parenthesis bold minus bold 2 bold right parenthesis bold plus bold 12 bold left parenthesis bold 3 bold right parenthesis bold minus bold 3 bold left parenthesis bold minus bold 4 bold right parenthesis bold plus bold d bold equals bold 0 bold rightwards double arrow bold d bold equals bold minus bold 40 bold So bold space bold the bold space bold equation bold space bold of bold space bold the bold space bold plane bold space bold is bold 4 bold x bold plus bold 12 bold y bold minus bold 3 bold z bold minus bold 40 bold equals bold 0 bold The bold space bold equation bold space bold of bold space bold the bold space bold line bold space bold given bold space bold is bold space fraction numerator bold x bold plus bold 2 over denominator bold 3 end fraction bold equals fraction numerator bold y bold plus begin display style bold 3 over bold 2 end style over denominator bold 2 end fraction bold equals fraction numerator bold z bold plus begin display style bold 4 over bold 3 end style over denominator begin display style bold 5 over bold 3 end style end fraction bold equals bold r bold rightwards double arrow bold x bold equals bold 3 bold r bold minus bold 2 bold comma bold space bold y bold equals bold 2 bold r bold minus bold 3 over bold 2 bold comma bold space bold z bold equals bold 5 over bold 3 bold r bold minus bold 4 over bold 3 bold Substituting bold space bold these bold space bold values bold space bold in bold space bold 4 bold x bold plus bold 12 bold y bold minus bold 3 bold z bold minus bold 40 bold equals bold 0 bold 4 open parentheses bold 3 bold r bold minus bold 2 close parentheses bold plus bold 12 open parentheses bold 2 bold r bold minus bold 3 over bold 2 close parentheses bold minus bold 3 open parentheses bold 5 over bold 3 bold r bold minus bold 4 over bold 3 close parentheses bold minus bold 40 bold equals bold 0 bold rightwards double arrow bold 31 bold r bold equals bold 62 bold rightwards double arrow bold r bold equals bold 2 bold The bold space bold coordinates bold space bold of bold space bold the bold space bold pointof bold space bold intersection bold space bold are bold x bold equals bold 4 bold comma bold space bold y bold equals bold 5 over bold 2 bold comma bold space bold z bold equals bold 2 bold Distance bold space bold between bold space bold left parenthesis bold minus bold 2 bold comma bold space bold 3 bold comma bold space bold minus bold 4 bold right parenthesis bold space bold and bold space bold left parenthesis bold 4 bold comma bold space bold 5 over bold 2 bold comma bold space bold 2 bold right parenthesis bold space bold is square root of bold 6 to the power of bold 2 bold plus bold 1 over bold 2 to the power of bold 2 bold plus bold 6 to the power of bold 2 end root bold equals square root of bold 289 over bold 4 end root bold equals bold 17 over bold 2

Answered by satyajit samal | 24th Dec, 2015, 03:29: PM