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Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry5 Marks
Question
Find the value of $\lambda,$ so that the lines $\frac{1-\text{x}}{3}=\frac{\text{7}\text{y}-14}{\lambda}=\frac{\text{z}-3}{2}$ and $=\frac{7-7\text{x}}{3\lambda}=\frac{\text{y}-5}{1}=\frac{6-\text{z}}{5}$ are at right angles. Also, find whether the lines are intersecting or not.
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Answer

Given lines are $\frac{1-\text{x}}{3}=\frac{\text{7}\text{y}-14}{\lambda}=\frac{\text{z}-3}{2}$ and $=\frac{7-7\text{x}}{3\lambda}=\frac{\text{y}-5}{1}=\frac{6-\text{z}}{5}$
Converting them into standard form,
we have $=\frac{\text{x}-1}{-3}=\frac{\text{y}-2}{\Big(\frac{\lambda}{7}\Big)}=\frac{\text{z}-3}{2}$ and $\frac{\text{x}-1}{\Big(\frac{-3\lambda}{7}\Big)}=\frac{\text{y}-5}{1}=\frac{\text{z}-6}{-5}$

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