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Let vec(AD) be the angle bisector of the...

Let `vec(AD)` be the angle bisector of the angle A of `DeltaABC`, then `vec(AD) = alphavec(AB) + betavec(AC)`, where

A

`alpha= (|vec(AB)|)/(|vec(AB)|+|vec(AC)|),beta=(|vec(AC)|)/(|vec(AB)|+|vec(AC)|)`

B

`alpha= (|vec(AB)|+|vec(AC)|)/(|vec(AB)|),beta=(|vec(AB)|+|vec(AC)|)/(|vec(AC)|)`

C

`alpha= (|vec(AC)|)/(|vec(AB)|+|vec(AC)|),beta=(|vec(AB)|)/(|vec(AB)|+|vec(AC)|)`

D

`alpha= (|vec(AB)|)/(|vec(AC)|),beta=(|vec(AC)|)/(|vec(AB)|)`

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, AD divides BC in the ratio AB : AC.
`therefore vec(AD)=(|vec(AB)|vec(AC)+|vec(AC)|vec(AB))/(|vec(AB)|+|vec(AC)|)`
`rArrvec(AD)=alpha vec(AB)+beta vec(AC),` where
`alpha= (|vec(AC)|)/(|vec(AB)|+|vec(AC)|) and beta=(|vec(AB)|)/(|vec(AB)|+|vec(AC)|)`
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OBJECTIVE RD SHARMA ENGLISH-ALGEBRA OF VECTORS-Chapter Test
  1. Let vec(AD) be the angle bisector of the angle A of DeltaABC, then vec...

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  2. If the vectors vec a =2hati + 3hatj +6hatk and vec b are collinear and...

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  3. If vec a , vec b , vec c are three non-zero vectors (no two of which ...

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  4. Vectors vec aa n d vec b are non-collinear. Find for what value of ...

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  5. If the diagonals of a parallelogram are 3 hati + hatj -2hatk and hati ...

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  6. If ABCD is a quadrilateral, then vec(BA) + vec(BC)+vec(CD) + vec(DA)=

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  7. The points with position vectors 60hati+3hatj,40hati-8hatj, ahati-52ha...

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  8. If ABCDEF is a regualr hexagon, then vec(AC) + vec(AD) + vec(EA) + ve...

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  9. In a regular hexagon ABCDEF, vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)=k...

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  10. If P, Q , R are the mid-points of the sides AB, BC and CA of Delta AB...

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  11. If G is the centroid of the DeltaABC and if G' is the centroid of anot...

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  12. In a quadrilateral ABCD, vec(AB) + vec(DC) =

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  13. If ABCDE is a pentagon, then vec(AB) + vec(AE) + vec(BC) + vec(DC) +...

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  14. If ABCD is a parallelogram, then vec(AC) - vec(BD) =

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  15. In a Delta ABC, " if " vec(AB) = hati - 7hatj + hatk and vec(BC) = 3 ...

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  16. If vectors vec(AB) = -3hati+ 4hatk and vec(AC) = 5hati -2hatj+4hatk ar...

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  17. The position vectors of P and Q are respectively vec a and vec b . If ...

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  18. If the points whose position vectors are 2hati + hatj + hatk , 6hati -...

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  19. The ratio in which hati + 2 hatj + 3 hatk divides the join of -2hati ...

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  20. If OACB is a parallelogrma with vec( OC) = vec(a) and vec( AB) = vec(...

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  21. The position vectors of the points A, B, C are 2 hati + hatj - hatk , ...

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