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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

OABC is a tetrahedron in which O is the origin and position vector of points A , B , C are i +2 j +3 k , 2 i + j + k and i +3 j +2 k respectively. An integral value of for which shortest distance between O A and B C is 3 2 is _______

Correct answer

3

Step-by-step solution

Unit vector ( n ) perpendicular to O A and C B n = CB OA | CB OA | = (3 -7) i -4 j +(5- ) k (3 -7)^2+16+(5- )^2 As CB OA = | array ccc i & j & k 1 & -3 & -1 1 & 2 & 3 array |=| BA n |= | (7-3 )-4(2- )+2(5- ) (3 -7)^2+16+(5+ )^2 | Shortest distance =| BA n |

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