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For three vectors `vec(a),vec(b)` and `vec( c ),vec(a)+vec(b)+vec( c )=vec(0)|vec(a)|=3,|vec(b)|=4,|vec( c )|=5`, then evaluate
`2(vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a))`.

A

100

B

50

C

`-25`

D

`-50`

Text Solution

Verified by Experts

The correct Answer is:
D
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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. If bar(a),bar( c ) and bar(d) are not coplanar vectors and bar(d).(bar...

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  2. If 4bar(a)+5bar(b)+9bar( c )=0 then (bar(a)xx bar(b))xx[(bar(b)xx bar(...

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  3. vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx v...

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  4. If vec(a) is a unit vector and vec(b)=(2,1,-1) and vec( c )=(1,0,3). T...

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  5. The volume of the parallelepiped with edges -12hati+alpha hatk,3hatj-h...

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  6. bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….

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  7. vec(a)|vec(b) and vec(c),|vec(a)|=2,|vec(b)|=3,|vec( c )|=4. The angle...

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  8. (vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )). If vec(a)*ve...

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  9. vec(u),vec(v) and vec(w) are not co-planar vectors and p and q are rea...

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  10. Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(...

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  11. Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(...

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  12. Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(...

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  13. Measure of the angle between the vector vec(a)=hati-hatj+hatk and vec(...

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  14. If vec(a)=hati+2hatj+hatk and vec(b)=hati-2hatj-3hatk then (vec(a)+vec...

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  15. Find the area of a parallelogram whose adjacent sides are given by the...

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  16. Let |vec(x)|=|vec(y)|=|vec(x)+vec(y)| =1 and if measure of the angle b...

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  17. hati*(hatkxx hatj)+hatj*(hati xx hatk)+hatk*(hatj xx hati)+hati*(hati ...

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  18. For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=ve...

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  19. A vector vec(a)=alpha hati+2hatj+beta hatk(alpha, beta in R) lies in t...

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  20. Let vec(a),vec(b) and vec( c ) be three unit vectors such that vec(a),...

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