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InterviewSolution
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Which of the following is the correct formula for the distance between the parallel lines l1 and l2?(a) d=\(\left|\frac{\vec{a_2}+\vec{a_1})×(\vec{a_2}-\vec{a_1})}{|\vec{b}|}\right |\)(b) d^2=\(\left|\frac{\vec{b}×(\vec{a_2}-\vec{a_1})}{|\vec{b}|}\right |\)(c) 2d=\(\left|\frac{\vec{b}×(\vec{a_2}-\vec{a_1})}{|\vec{b}|}\right |\)(d) d=\(\left|\frac{\vec{b}×(\vec{a_2}-\vec{a_1})}{|\vec{b}|}\right |\)This question was addressed to me in examination.I want to ask this question from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12 |
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Answer» CORRECT option is (d) d=\(\left|\frac{\vec{b}×(\vec{a_2}-\vec{a_1})}{|\vec{b}|}\RIGHT |\) The explanation is: If L1 and L2 are two parallel lines, then they are coplanar and hence can be represented by the FOLLOWING equations \(\vec{r}=\vec{a_1}+λ\vec{b}\) \(\vec{r}=\vec{a_2}+μ\vec{b}\) Then the distance between the lines is given by d=\(\left|\frac{\vec{b}×(\vec{a_2}-\vec{a_1})}{|\vec{b}|}\right |\) |
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