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If vectors baraequiv(a(1),a(2),a(3)) and...

If vectors `baraequiv(a_(1),a_(2),a_(3))` and `barbequiv(b_(1),b_(2),b_(3))` are collinear/coincident/parallel, then, in general,

A

`a_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3)=0`

B

`(a_(1))/(b_(1))+(a_(2))/(b_(2))+(a_(3))/(b_(3))`=0

C

`(a_(1))/(a_(2))=(b_(1))/(b_(2))=(a_(3))/(b_(3))`=0

D

`(a_(1))/(b_(1))=(a_(2))/(b_(2))=(a_(3))/(b_(3))`=0

Text Solution

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The correct Answer is:
D
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MARVEL PUBLICATION-VECTORS-TEST YOUR GRASP
  1. If vectors baraequiv(a(1),a(2),a(3)) and barbequiv(b(1),b(2),b(3)) are...

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  2. If ABCDEF is a regular hexagon , then bar(AB) + bar(AC) + bar(AE) + ...

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  3. If the origin is the centroid of a triangle ABC having vertices A(a ,1...

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  4. If alpha,beta ,gamma are direction angles of a line , then cos 2alpha ...

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  5. If |bar(u)| = sqrt(3) and bar(u) is equally inclined to co - ordinate...

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  6. If vectors 2i-j+k,i+2j-3k and 3i+aj+5k are coplaner, then a=

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  7. If bara.i = 4, then bara.[j xx (2j - 3k)]=

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  8. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

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  9. If veca vecb are non zero and non collinear vectors, then [(veca, vecb...

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  10. If bara,barb,barc are non-coplaner vectors and barp=(barbxxbarc)/([bar...

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  11. If direction ratios of two lines are 2,-6,-3 and 4,3,-1 then directi...

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  12. If the volumes of parallelepiped with coterminus edges -pj+5k,i-j+qk a...

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  13. A line makes 45^(@) with OX, and equal angles with OY and OZ. Then the...

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  14. If the points with position vectors -i + 3j + 2k , -4i + 2j - 2k and 5...

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  15. If bara.barb=barb.barc=barc.bara=0 and bara,barb,barc form a right-han...

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  16. If bara,barb,barc are non-coplaner vectors, then (bara.(barbxxbarc))/...

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  17. i · (j xx k) + j · (k xx i) + k · (i xx j ) =

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  18. If bara=2i+3j-k,barb=-i+2j-4k and barc=i+j+k, then (baraxxbarb).(barax...

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  19. If vectors 2hati-hatj+hatk ,hati+2hatj-3hatk and 3hati+mhatj+5hatk are...

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  20. 2i · (j xx k) - 3j · (i xx k) - 4k · (i xx j) =

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  21. If vectors bara,barb,barc are non-coplaner, then ([bara+2barb barb+2...

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