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a and b are the position vectors of the points A and B with respect to an origin O. A point C on OA is such that `2AC = CO, CD` is parallel to OB and `|vecCD| = 3 |vecOB|` , then the vector `vecAD` is ..........

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The correct Answer is:
`3b -(1)/(3)a`
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Let A and B be points with position vectors veca and vecb with respect to origin O. If the point C on OA is such that 2vec(AC)=vec(CO), vec(CD) is parallel to vec(OB) and |vec(CD)|=3|vec(OB)| then vec(AD) is (A) vecb-veca/9 (B) 3vecb-veca/3 (C) vecb-veca/3 (D) vecb+veca/3

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coplanar for 1 ) all except two values of ? 2) all except one value of ? 3) forall values of? 4) no value of? 12. TRIANGLE AND PARALLELOGRAM LAW, VECTOR ADDITION: 7. The value of 'a', for which the points A, B, C with position vectors 27-j+k, i-3j -5k and ai -37+k are the vertices of a right angled triangle with C are [AIE-2006] |13 1)-2 and 1 3) 2 and 1 2) 2 and -1 4)-2 and -1 SCALAR MULTIPLICATION AND 14. THEIR PROPERTIES Let A and B be points with position vectors a and b with respect to origin O. If the point C' on OA is such that 2AC CO, CD Is parallel to OB and CD 3OB then AD is parallel to OB and 0-3|OR then AD is 3 1) b 3 2) a A 158

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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Self Assessment Test (MULTIPLE CHOICE QUESTIONS)
  1. The vector 2i + 3j - 4k and ai + bj + ck are perpendicular if

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  2. If a and b are position vectors of A and B respectively the position v...

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  3. a and b are the position vectors of the points A and B with respect to...

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  4. If A = 2i + 2j-k, B = 6i-3j+2k, then A xx B will be given by

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  5. The number of vectors of unit length perpendicular to vectors vec ...

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  6. A vector a has components 2p and 1 with respect to a rectangular cart...

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  7. If |vecalpha + vecbeta| = |vecalpha - vecbeta|, then

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  8. If veca and vecb are two vectors such that veca.vecb = 0 and veca xx v...

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  9. Let veca, vecb, vecc be three non-coplanar vectors and vecp,vecq,vecr ...

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  10. The components of a vector veca along and perpendicular to a non-zero ...

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  11. For any three vectors a, b, c (a-b).{(b-c) xx (c-a)} = 2a.(bxxc). ...

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  12. If a = 4i + 6j and b = 3j+4k, then the vector form of component of a a...

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  13. A unit vector perpendicular to the vector 4i-j+3k and -2i+j-2k is

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  14. The unit vector perpendicular to the two vectors i-j and i+2j, and per...

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  15. If u = i xx (a xx i), + j xx (a xx j) + k xx(a xx k), then

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  16. The volume of a parallelopiped whose sides are given by vecOA =2i-3j,v...

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  17. If alpha = 2i + 3j - k, beta = -i + 2j-4k, gamma = i+j+k then the valu...

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  18. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

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  19. If the vectors vec c , vec a=x hat i+y hat j+z hat ka n d vec b= hat ...

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

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