Which of the below given is the correct formula for the distance between two skew lines l1 and l2?

Category: QuestionsWhich of the below given is the correct formula for the distance between two skew lines l1 and l2?
Editor">Editor Staff asked 11 months ago

Which of the below given is the correct formula for the distance between two skew lines l1 and l2?
 
(a) d=\(\left |\frac{(\vec{b_1}×\vec{b_2}).(a_2-a_1)}{|\vec{b_1}×\vec{b_2}|}\right |\)
 
(b) 2d=\(\left |\frac{(\vec{b_1}-\vec{b_2}).(a_2-a_1)}{|\vec{b_1}-\vec{b_2}|}\right |\)
 
(c) d=\(\left |\frac{(\vec{b_1}×\vec{b_2}).(a_2.a_1)}{3|\vec{b_1}×\vec{b_2}|}\right |\)
 
(d) d^2=\(\left |\frac{(\vec{b_1}×\vec{b_2}).(a_2-a_1)}{|\vec{b_1}-\vec{b_2}|}\right |\)
 
This question was addressed to me during an online interview.
 
I need to ask this question from Three Dimensional Geometry topic in division Three Dimensional Geometry of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct answer is (a) d=\left |\frac{(\vec{b_1}×\vec{b_2}).(a_2-a_1)}{|\vec{b_1}×\vec{b_2}|}\right |
 
Easy explanation: The distance between two lines l1 and l2 with the equations
 
\vec{r}=\vec{a_1}+λ\vec{b_1}
 
\vec{r}=\vec{a_2}+μ\vec{b_2}
 
Then, the distance between the two lines is given by the formula
 
d=\left |\frac{(\vec{b_1}×\vec{b_2}).(a_2-a_1)}{|\vec{b_1}×\vec{b_2}|}\right |