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A, B, C and D have position vectors veca...

A, B, C and D have position vectors `veca, vecb, vecc and vecd`, repectively, such that `veca-vecb = 2(vecd-vecc)`. Then

A

AB and CD bisect each other

B

BD and AC bisect each other

C

AB and CD trisect each other

D

BD and AC trisect each other

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The correct Answer is:
D
`veca-vecb= 2(vecd-vecc)`
`therefore (veca+ 2vecc)/(2+1) = (vecb+ 2vecd)/(2+1)` ltBrgt Hence, AC and BD trisect each other as L.H.S is the position vector of a point trisecting A an C, and R.H.S that of B and D.
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CENGAGE-INTRODUCTION TO VECTORS -Exercise (Single)
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  2. The vector vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are sides...

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  3. A, B, C and D have position vectors veca, vecb, vecc and vecd, repecti...

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  4. If veca and vecb are two unit vectors and theta is the angle between t...

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  5. let us define , the length of a vector as |a| + |b| +|c| . this defini...

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  6. Given three vectors veca=hati-3hatj,vecb=2hati-thatj and vecc=-2hati+2...

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  7. If vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vec...

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  8. In triangle A B C ,/A=30^0,H is the orthocenter and D is the midpoint ...

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  9. Let vecr1, vecr2,……vecrn be the position of points P1,P2,………,Pn respec...

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  10. Given three non-zero, non-coplanar vectors veca, vecb and vecc. vecr1=...

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  11. If the vectors vec a and vec bare linearly independent and satisfying ...

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  12. In a trapezium ABCD the vector B vec C = lambda vec(AD). If vec p = ...

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  13. Vectors veca = hati+2hatj+3hatk, vec b = 2hati-hatj+hatk and vecc= 3ha...

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  14. Vectors vec a=-4 hat i+3 hat k ; vec b=14 hat i+2 hat j-5 hat k are l...

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  15. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

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  16. If 4hati+ 7hatj+ 8hatk, 2hati+ 3hatj+ 4hatk and 2hati+ 5hatj+7hatk are...

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  17. If vec b is a vector whose initial point divides thejoin of 5 hat ...

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  18. The value of the lambda so that P, Q, R, S on the sides OA, OB, OC and...

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  19. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

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  20. Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB...

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