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The position vectors of the points A,B,C...

The position vectors of the points A,B,C,D are `vec(3i)-vec(2j)-veck, vec(2i)+vec(3j)-vec(4k)-veci+vecj+vec(2k) and vec(4j) +vec(5j)+vec(lamdak)` respectively Find lamda if A,B,C,D are coplanar.

A

`(53)/17)`

B

`-(146)/(17)`

C

`(230)/(17)`

D

none

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The correct Answer is:
B
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. If a, b and c are non-zero vectors such that a times b=c, b times c=a ...

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  2. a =2i-j+k, b=i+2j-3k, c=3i+lambdaj+5k and if these vectors be coplanar...

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  3. The position vectors of the points A,B,C,D are vec(3i)-vec(2j)-veck, v...

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  4. The value of lambda for which the points L(1,0,3), M(-1,3,4),N(1,2,1) ...

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  5. If veca lies in the plane of vectors vecb and vecc, then which of the ...

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  6. IF r.a = 0, r. b = 0 and r. c= 0 for some non-zero vector r. Then, the...

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  7. If a, b,c are non-coplanar vectors such that r.a = r.b = r.c =0, then

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  8. Blank,

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  9. If |[a, b, c], [a^(2), b^(2), c^(2)], [a^(3)+1, b^(3)+1, c^(2)+1]|=0 a...

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  10. If the vectors ai + j + k , i + bj + k and i + j + ck, where a, b, c n...

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  11. Another form (1+a)/(1-a) + (1+b)/(1-b) + (1 +c)/(1-c) =

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  12. If the vectors ai +j + k , i-bj+k, i+j-ck are co-planar, then abc + 2 ...

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  13. If the vector ai+j+k,i+bj+k and i+j+ck are coplanar, then :

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  14. Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj...

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  15. If veca , vecb , vec c are any three coplanar unit vectors , then :

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  16. If veca, vecb, vecc are three non-coplanar mutually perpendicular unit...

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  17. The vector vec(a) lies in the plane of vectors vec(b) and vec(c). Whi...

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  18. If a = i-j+k,b=i-2j-k and c=3i+pj+5k are coplanar, then p =

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  19. If l( b xx c) + m(c xxa) + n(a xx b) = 0 and at least one of l, m, n i...

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  20. The vectors (x,x+1,x+2),(x+3,x+3,x+5) and (x+6,x+7,x+8) are coplanar f...

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