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  • Let a line having direction ratios   intersect the lines <img alt="\mathrm{\fr

Let a line having direction ratios \mathrm{1,-4,2}  intersect the lines \mathrm{\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1} \quad and \quad \frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}}  at the points \mathrm{A} and \mathrm{B}. Then  \mathrm{(A B)^{2}} is equal to _________.

Option: 1

84


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer



Direction ratio's of AB:

\mathrm{\frac{3\mu-2\lambda +7}{1}= \frac{-\mu -3\lambda-6 }{-4}= \frac{\mu -\lambda -2}{2}}
On solving \mathrm{\mu = -5}
                  \mathrm{\lambda = -3}

\mathrm{\therefore \; \; \left ( AB \right )^{2}= \left ( -15+6+7 \right )^{2}+\left ( 5+9-6 \right )^{2}+\left ( -5+3-2 \right )^{2}}
                      \mathrm{= 4+64+16}
                       \mathrm{= 84}

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manish

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