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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

If a , b , c and d are the position vectors of the points A, B, C and D respectively in three dimensional space no three of A, B, C, D are collinear and satisfy the relation 3 a -2 b + c -2 d = 0 , then :

Options

  1. AA, B, C and D are coplanar
  2. BThe line joining the points B and D divides the line joining the point A and C in the ratio 2: 1 .
  3. CThe line joining the points A and C divides the line joining the points B and D in the ratio 1: 1 .
  4. DThe four vectors a , b , c and d are linearly dependents.

Correct answer

D. The four vectors a , b , c and d are linearly dependents.

Step-by-step solution

3 a -2 b + c -2 d =0 sum of coefficient =0 a , b , c , d are coplanar Also 2 b +2 d =3 a + c b + d 2 = 3 a + c 4

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