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In a regular hexagon ABCDEF, prove that ...

In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

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Verified by Experts

The correct Answer is:
B
By triangle law, `AB=AD-BD,AC=AD-CD`

Therefore, `AB+AC+AD+AE+AF`
`=3AD+(AE-BD)+(AF-CD)=3AD`
hence, `lamda=3" "(becauseAE=BD,AF=CD)`
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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  2. Find the discriminant of the quadratic equation x^2+3x+2

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  3. In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

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  4. Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3...

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  5. If a and b are two non-zero and non-collinear vectors then a+b and a-b...

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  6. If |veca+ vecb| lt | veca- vecb|, then the angle between veca and vecb...

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  7. The magnitudes of mutually perpendicular forces a,b and c are 2,10 and...

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

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  9. Find the discriminant of the quadratic equation x^2+5x+4=0 and also fi...

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  10. Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja ...

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

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  12. If vecx and vecy are two non-collinear vectors and ABC is a triangle w...

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  13. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

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  14. If the resultant of two forces is equal in magnitude to one of the ...

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  15. If vec b is a vector whose initial point divides the join of 5 hat ...

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  16. find the term independent of x in the expansion of (2x-1/x)^2 ?

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

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

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  19. if alpha and beta are the root of the quadratic polynomial f(x) = x^2-...

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  20. If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then t...

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