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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Given a tetrahedron D-A B C with A B=12, C D=6 . If the shortest distance between the skew lines A B and C D is 8 and the angle between them is 6 , then find the volume of tetrahedron.

Correct answer

48

Step-by-step solution

Given | b - a |=12 ; | c |=6 Equation of CD is r = c & eq. of A B is r = a + ( b - a ) S.D. = | a c ( b - a ) c ( b - a ) |=8 aligned & | [ array lll a & c & b array ] c ( b - a ) |=8 & | [ array lll a & c & b array ] |=8| c ( b - a )| & 6 ~V = 8| c || b - a | 2 & 6 ~V =(4)(6)(12) V=48 aligned

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