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If veca,vecb,vecc & vecd are position ve...

If `veca,vecb,vecc & vecd` are position vector of point A,B,C and D respectively in 3-D space no three of A,B,C,D are collinnear and satisfy the relation `3veca-2vecb+vecc-2vecd=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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VK JAISWAL-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-2 : One or More than One Answer is/are Correct
  1. If veca=hati+6hatj+3hatk, vecb=3hati+2hatj+hatk and vec c=(alpha+1)hat...

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  2. Consider the lines: L1:(x-2)/1=(y-1)/7=(z+2)/-5, L2:x-4=y+3=-z Then wh...

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  3. Let hata, hatb and hatc be three unit vectors such that hata=hatb+(h...

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  4. The value(s) of mu for which the straight lines vecr=3hati-2hatj-4hatk...

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  5. If hati xx [ (veca-hatj) xxhati]+ hatj xx [(veca - hatk)xx hatj] +hatk...

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  6. The value of expression [veca xx vecb" "vec c xx vecd" " vece xx vecf...

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  7. If veca,vecb,vecc & vecd are position vector of point A,B,C and D resp...

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  8. If OAB is a tetrahedron with edges and hatp, hatq, hatr are unit vect...

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  9. Let hata and hatc are unit vectors and |vecb|=4. If the angle between...

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  10. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

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

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

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

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  14. The volume of a right triangular prism ABCA1B1C1 is equal to 3. If the...

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  15. If veca=x hati+y hatj+z hatk, vecb=y hati+z hatj+x hatk, and vec c=z ...

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

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

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  18. The solution vectors vecr of the equation vecr xx hati=hatj+hatk and v...

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  19. Which of the following statement(s) is/are incorrect ?

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  20. The lines with vector equations are, vecr(1)=3hati+6hatj+lambda(-4hat...

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