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If veca=hati+6hatj+3hatk, vecb=3hati+2ha...

If `veca=hati+6hatj+3hatk, vecb=3hati+2hatj+hatk and vec c=(alpha+1)hati+(beta-1)hatj+hatk` are linearly dependent vectors and `|vec c|=sqrt(6)`, then the possible value(s) of `(alpha+beta)` can be : (a) 1 (b) 2 (c) 3 (d) 4

A

1

B

2

C

3

D

4

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The correct Answer is:
A, C
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VIKAS GUPTA (BLACK BOOK) ENGLISH-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-2 : One or More than One Answer is/are Correct
  1. If equation of three lines are : (x)/(1)=(y)/(2)=(z)/(3), (x)/(2)=...

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  2. If veca=hati+6hatj+3hatk, vecb=3hati+2hatj+hatk and vec c=(alpha+1)hat...

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

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

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  6. If hati xx[(veca-hatj)xxhati]xx[(veca-hatk)xxhatj]+veckxx[(veca-veci)x...

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  7. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  8. If vec a ,vec b,vec c and vec d are the position vectors of the point...

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

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  10. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

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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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  12. Let vecr=(veca xx vecb)sinx+(vecb xx vec c)cosy+2(vec c xx vec a), whe...

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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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  16. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc=...

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

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

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