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If the middle points of sides BC, CA and AB of triangle ABC are respectively D,E ,F then position vector of centre of triangle DEF, when position vector of A, B , C are respectively `hati + hatj, hatj + hatk , hatk + hati ` is

A

`1/3 (hati + hatj + hatk)`

B

`(hati + hatj + hatk)`

C

`2(hati + hatj + hatk)`

D

`2/3 (hati + hatj + hatk)`

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The correct Answer is:
D
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DISHA PUBLICATION-VECTOR ALGEBRA-EXERCISE -1 : CONCEPT BUILDER
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  7. If veca , vecb , vec c are any three coplanar unit vectors , then :

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  8. The vector veca=alpha hati+2hatj+betahatk lies in the plane of vectors...

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  9. Let vecu= hati+hatj, vecv = hati -hatj and vecw = hati+2hatj+3hatk. I...

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  10. If vectors a=4hat(i)-3hat(j)+6hat(k) and vector b=-2hat(i)+2hat(j)-hat...

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  11. A vector of magnitude 14 lies in the xy-plane and makes an angle of 60...

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  12. If veca,vecb,vec c are unit vectors such that veca+vecb+vec c= vec0 fi...

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  13. The two variable vectors 3xhati+yhatj-3hatk and xhati-4yhatj+4hatk are...

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  14. Angle between the vectors sqrt3(veca xx vec b) " and " vec b - (veca ....

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  15. If the vector veca = (2 ,log3 x ,a ) and vecb = (-3,a log3x,log3x) are...

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  16. If veca , vecb ,vec c are the 3 vectors such that |veca| = 3, |vecb| ...

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  17. The vectors (2hati - mhatj+ 3mk) and {(1 + m) hati -2m hatj + hatk} i...

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  18. Let veca , vecb , vecc be three unit vectors such that |veca + vecb +...

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  19. If veca,vecb and vecc are three vectors of which every pair is non col...

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  20. The two vectors (x^2 - 1)hati +(x+2)hatj + x^2 hatk and 2hati -xhatj +...

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