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If the points A, B, C and D with positio...

If the points A, B, C and D with position vectors `overset(^)i+overset(^)j+overset(^)k,2overset(^)i+3overset(^)j+overset(^)k,overset(^)i+2overset(^)j+5overset(^)k and lambdaoverset(^)i+3overset(^)j+4overset(^)k` are coplanar then `lambda` is equal to

A

5

B

7

C

2

D

`13/8`

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The correct Answer is:
D
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TARGET PUBLICATION-VECTORS-Critical Thinking
  1. In DeltaABC, P is the mid point of BC,Q divides CA internally in the r...

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  2. If overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + ...

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  3. If the points (1,1,2),(2,1,p),(1,0,3) and (2,2,0) are co-planar then ...

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  4. If the points A, B, C and D with position vectors overset(^)i+overset(...

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  5. If aoverset(^)i+overset(^)j+overset(^)k,overset(^)i-boverset(^)j+overs...

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  6. If the given vectors (-bc,b^2+bc,c^2+bc)(a^2+ac,-ac,c^2+ac) and (a^2+a...

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  7. If bara,barb,barc are non-zero, non collinear vectors, then the vector...

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  8. Given vectors bara,barb,barc such that bara.(barbxxbarc)=lambda!=0 the...

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  9. For any three vectors bara,barb and barc,(bara-barb)[(barb+barc)xx(bar...

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  10. If bara,barb and barc are three non-coplanar vectors, then : (bara + b...

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  11. If bar r=l(bar b xx bar c)+m(bar c xx bar a)+n(bar a xx bar b) and [...

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  12. The volume of parallelopiped with vector bara+2barb-barc,bara-barb and...

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  13. If the volume of parallelopiped with coterminus edges -poverset(^)i+5k...

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  14. If the volumes of tetrahearon where vertices (1,2,0),(2,0,4),(-1,2,0) ...

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  15. If D is the mid -point of side AB of DeltaABC, then bar(AB) + bar(BC)...

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

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  17. If G and Gprime are the centroids of the triangle ABC and AprimeBprime...

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  18. If S is circumcentre, O is orthocentre of DeltaABC, then vec(SA)+vec(...

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  19. If A(-3,-2,0),B(3,-3,1) and C(5,0,2) are three successive vertices of...

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  20. In a trapezium, if the vectors bar(BC)=lambda(AD),barP=bar(AC)+bar(BD)...

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