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If vec a ,vec b,vec c and vec d are the...

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

A

A, B, C and D are coplanar

B

The line joining the points B and D divides the line joining the point A and C in the ratio of `2:1`

C

The line joining the points A and C divides the line joining the points B and D in the ratio of `1:1`

D

The four vectors `veca, vecb, vec c and vecd` are linearly dependent .

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The correct Answer is:
A, C, D
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VIKAS GUPTA (BLACK BOOK) ENGLISH-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-2 : One or More than One Answer is/are Correct
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  11. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

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  13. If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd, wh...

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  14. Let a be a real number and vec alpha = hati +2hatj, vec beta=2hati+a h...

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  15. The volume of a right triangular prism ABCA(1)B(1)C(1) is equal to 3 c...

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  17. If a line has a vector equation, vecr=2hati +6hatj+lambda(hati-3hatj) ...

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  18. Let M,N, P and Q be the mid points of the edges AB, CD, AC and BD resp...

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