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In fig. A B ,D Ea n dG F are parallel to...

In fig. `A B ,D Ea n dG F` are parallel to each other and `A D ,B Ga n dE F` are parallel to each other. If `C D : C E=C G : C B=2:1,` then the value of area `( A E G):` area `( A B D)` is equal to `7//2` b. `3` c. `4` d. `9//2`

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 PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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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 vec a is parallel to vec bxx vec c , then ( vec axx vec b).( vec ...

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  8. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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

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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 formed by the coterminous edges vec a ...

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  13. If vec a , vec b , and vec c are three mutually orthogonal unit vector...

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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(1)hati+b(2)hatj+b(3)hatk an...

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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= la...

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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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