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For any vectors vec(a),vec(b) and vec( c...

For any vectors `vec(a),vec(b)` and `vec( c )`. Out of the following, which statement is true ?

A

`vec(a)xx(vec(b)xx vec( c ))=(vec(a)xx vec(b))xx vec( c )`

B

`vec(a)xx vec(b)=vec(b)xx vec(a)`

C

`vec(a).(vec(b)xx vec( c ))=(vec(a).vec(b))xx(vec(a).vec( c ))`

D

`vec(a).(vec(b)-vec( c ))=vec(a).vec(b)-vec(b).vec( c )`

Text Solution

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The correct Answer is:
D
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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. In a parallelogram ABCD, vec(AB)=hati+hatj+hatk and diagonal vec(AC)=h...

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  2. The points A(vec(a)),B(vec(b)) and C(vec( c )) are collinear then …………...

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  3. For any vectors vec(a),vec(b) and vec( c ). Out of the following, whic...

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  4. bar(a)=2hati+hatj-2hatk and bar(b)=hati+hatj. The vector bar( c ) is s...

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  5. In a quadrilateral ABCD, vec(AB)=vec(b),vec(AD)=vec(d) and vec(AC)=m v...

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  6. If vec(a)=2hati+hatj+x hatk and vec(b)=hati+hatj-hatk then the minimum...

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  7. If vec(a).hati=4 then (vec(a)xx hatj).(2hatj-3hatk)= ………..

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  8. vec(a),vec(b) and vec( c ) are unit vectors vec(a)xx(vec(b)xx vec( c )...

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  9. If vec(u)=hati xx(vec(a)xx hati)+hatj xx(vec(a)xx hatj)+hatk xx(vec(a)...

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  10. For the vectors vec(x) and vec(y),vec(x)+vec(y)=vec(a),vec(x)xx vec(y)...

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  11. Vector vec(a)=hati-hatj,vec(b)=hati+hatj+hatk. The vector vec( c ) is ...

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  12. The vectors vec(a) and vec(b) are not perpendicular. The vectors vec( ...

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  13. vec(a)=hatj-hatk and vec( c )=hati-hatj-hatk. The vector vec(b) is suc...

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  14. For any vector vec(a),(vec(a)xx vec(i))^(2)+(vec(a)xx hatj)^(2)+(vec(a...

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  15. vec(a),vec(b) and vec( c ) are three vector vec(a)ne0 and |vec(a)|=|ve...

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  16. For any vecotr vec(a), The value of hati xx(vec(a)xx hati)+j xx(vec(a)...

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  17. If (a(1),1,1),(1,a(2),1) and (1,1,a(3)) are coplaner (where a(i)ge1,i=...

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  18. If bar(x)=(1,-1,0),bar(y)=(0,1,3) and bar(z)=(2,1,1) then bar(x)xx (ba...

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  19. If [vec(a)xx vec(b),vec(b)xx vec( c ),vec( c )xx vec(a)]=lambda[vec(a)...

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  20. The volume of a parallelepiped with edges vec(OA)=(3,1.4),vec(OB)=(1,2...

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