Solve the following question:

Asked by joykphukan | 23rd Dec, 2015, 06:26: PM

Expert Answer:

bold Let bold space bold the bold space bold equation bold space bold of bold space bold the bold space bold plane bold space bold passing bold space bold through bold space bold the bold space bold line bold space bold of bold space bold intersection bold space bold of bold space bold r with bold rightwards arrow on top bold. open parentheses bold 2 bold i with bold overbrace on top bold plus bold 6 bold j with bold overbrace on top close parentheses bold plus bold 12 bold plus bold lambda open square brackets bold r with bold rightwards arrow on top bold. open parentheses bold 3 bold i with bold overbrace on top bold minus bold j with bold overbrace on top bold plus bold 4 bold k with bold overbrace on top close parentheses close square brackets bold equals bold 0 bold rightwards double arrow bold r with bold rightwards arrow on top bold. open square brackets open parentheses bold 2 bold plus bold 3 bold lambda close parentheses bold i with bold hat on top bold plus open parentheses bold 6 bold minus bold lambda close parentheses bold j with bold hat on top bold plus bold 4 bold lambda bold k with bold hat on top close square brackets bold plus bold 12 bold equals bold 0 bold. bold. bold. bold left parenthesis bold 1 bold right parenthesis bold Writing bold space bold in bold space bold normal bold space bold form fraction numerator bold r with bold rightwards arrow on top bold. open square brackets open parentheses bold 2 bold plus bold 3 bold lambda close parentheses bold i with bold hat on top bold plus open parentheses bold 6 bold minus bold lambda close parentheses bold j with bold hat on top bold plus bold 4 bold lambda bold k with bold hat on top close square brackets over denominator square root of open parentheses bold 2 bold plus bold 3 bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 6 bold minus bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 4 bold lambda close parentheses to the power of bold 2 end root end fraction bold equals fraction numerator bold minus bold 12 over denominator square root of open parentheses bold 2 bold plus bold 3 bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 6 bold minus bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 4 bold lambda close parentheses to the power of bold 2 end root end fraction bold Distance bold space bold from bold space bold the bold space bold origin bold space bold equals open vertical bar fraction numerator bold minus bold 12 over denominator square root of open parentheses bold 2 bold plus bold 3 bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 6 bold minus bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 4 bold lambda close parentheses to the power of bold 2 end root end fraction close vertical bar open vertical bar fraction numerator bold minus bold 12 over denominator square root of open parentheses bold 2 bold plus bold 3 bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 6 bold minus bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 4 bold lambda close parentheses to the power of bold 2 end root end fraction close vertical bar bold equals bold 1 bold rightwards double arrow open parentheses bold 2 bold plus bold 3 bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 6 bold minus bold lambda close parentheses to the power of bold 2 bold plus open parentheses bold 4 bold lambda close parentheses to the power of bold 2 bold equals bold 144 bold rightwards double arrow bold 26 bold lambda to the power of bold 2 bold plus bold 40 bold equals bold 144 bold rightwards double arrow bold lambda to the power of bold 2 bold equals bold 4 bold rightwards double arrow bold lambda bold equals bold plus-or-minus bold 2 bold Using bold space bold the bold space bold value bold space bold of bold space bold lambda bold space bold in bold space bold left parenthesis bold 1 bold right parenthesis bold comma bold space bold we bold space bold get bold space bold the bold space bold equation bold space bold of bold space bold plane bold space bold as bold r with bold rightwards arrow on top bold. open square brackets open parentheses bold 2 bold plus-or-minus bold 6 close parentheses bold i with bold hat on top bold plus open parentheses bold 6 bold minus-or-plus bold 2 close parentheses bold j with bold hat on top bold plus-or-minus bold 8 bold k with bold hat on top close square brackets bold plus bold 12 bold equals bold 0 bold rightwards double arrow bold r with bold rightwards arrow on top bold. open parentheses bold 8 bold i with bold overbrace on top bold minus bold 4 bold j with bold overbrace on top bold plus bold 8 bold k with bold overbrace on top close parentheses bold plus bold 12 bold equals bold 0 bold space bold space bold or bold space bold r with bold rightwards arrow on top bold. open parentheses bold minus bold 4 bold i with bold hat on top bold plus bold 8 bold j with bold overbrace on top bold minus bold 8 bold k with bold overbrace on top close parentheses bold plus bold 12 bold equals bold 0 bold rightwards double arrow bold r with bold rightwards arrow on top bold. open parentheses bold 2 bold i with bold overbrace on top bold minus bold j with bold overbrace on top bold plus bold 2 bold k with bold overbrace on top close parentheses bold plus bold 3 bold equals bold 0 bold space bold space bold or bold space bold r with bold rightwards arrow on top bold. open parentheses bold minus bold i with bold hat on top bold plus bold 2 bold j with bold overbrace on top bold minus bold 2 bold k with bold overbrace on top close parentheses bold plus bold 3 bold equals bold 0 bold In bold space bold cartesian bold space bold form bold space bold 2 bold x bold minus bold y bold plus bold 2 bold z bold plus bold 3 bold equals bold 0 bold space bold or bold space bold minus bold x bold plus bold 2 bold y bold minus bold 2 bold z bold plus bold 3 bold equals bold 0

Answered by satyajit samal | 24th Dec, 2015, 04:10: PM