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Let A(1,-1,2) and B(2,3-1) be two points...

Let `A(1,-1,2) and B(2,3-1)` be two points. If a point P divides AB internally in the ratio `2:3`, then the position vector of P is

A

`1/sqrt5(overset(^)i+overset(^)j+overset(^)k)`

B

`1/sqrt3(overset(^)i+6overset(^)j+overset(^)k)`

C

`1/sqrt3(overset(^)i+overset(^)j+overset(^)k)`

D

`1/5(7overset(^)i+3overset(^)j+4overset(^)k)`

Text Solution

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The correct Answer is:
D
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TARGET PUBLICATION-VECTORS-Competitive Thinking
  1. If bara=overset(^)i+overset(^)j-2overset(^)k,barb=2overset(^)i-overset...

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  2. The position vectors of the point which divides internally in the rati...

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  3. Let A(1,-1,2) and B(2,3-1) be two points. If a point P divides AB inte...

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  4. If z1 and z2 are z co-ordinates of the point of trisection of the seg...

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  5. If the position vector of a point A is vec a + 2 vec b and vec a divi...

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  6. Assertion (A): If (-1,3,2) and (5,3,2) are respectively the orthocentr...

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  7. If the orthocentre and centroid of a triangle are (-3,5,2) and (3,3,4)...

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  8. L and M are two points with position vectors 2vec(a)-vec(b)andvec(a)+2...

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  9. The position vector of a point R which divides the line joining two po...

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  10. If 3barP+2barR-5barQ=bar0, then

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  11. If three points A,B,C are collinear, whose position vectors are overse...

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  12. Let square PQRS be a quadrilateral. If M and N are the mid-points of t...

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  13. In DeltaABC,L,M,N are points on BC,CA,AB respectively, dividing them i...

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  14. Let G be the centroid of a triangle ABC and O be any other point, then...

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  15. If A, B, C are the vertices of a triangle whose position vectros are v...

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  16. If bara=2overset(^)i+overset(^)j-overset(^)k,barb=overset(^)i+2overset...

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  17. If bara=overset(^)i+overset(^)j+overset(^)k,barb=2overset(^)i+lambdaov...

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  18. If bara is perpendicular to barb and barc,|bara|=2,|barb|=3,|barc|=4 ...

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  19. If bara,barb,barc are mutually prependicular vectors having megnitudes...

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  20. The value of [bara-barb,barb-barc,barc-bara], where |bara|=1,|barb|=5 ...

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