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In fig. 2.33 AB, DE and GF are parallel ...

In fig. 2.33 AB, DE and GF are parallel to each other and AD, BG and EF ar parallel to each other . If CD: CE = CG:CB = 2:1 then the value of area `(triangleAEG): area (triangleABD) ` is equal to

A

`7//2`

B

3

C

4

D

`9//2`

Text Solution

Verified by Experts

The correct Answer is:
b
Let A be the origin, `vec(AB) = veca , vec(AD) = vecb`
so, `vec(AE) , vecb + 3/2 veca, vec(AG) = veca + 3vecb`
`(1/2|(veca+3vecb)xx(vecb+3/2veca)|)/(1/2|vecaxxvecb|)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Position vector hat k is rotated about the origin by angle 135^0 i...

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  2. In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d ...

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  3. In fig. 2.33 AB, DE and GF are parallel to each other and AD, BG and E...

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  4. A unit vector veca in the plane of vecb=2hati+hatj and vecc=hati-hatj+...

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  5. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

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  6. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

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  7. If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vec...

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  8. about to only mathematics

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  9. If vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

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  10. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

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  11. If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

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  12. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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  13. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

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  14. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

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  15. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

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  16. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

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  17. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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  18. If veca, vecb and vecc are such that [veca vecb vecc] =1, vecc= lambda...

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  19. If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)...

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  20. Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec...

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