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Prove that (i) [hat(i)hat(j)hat(k)]=[h...

Prove that
(i) `[hat(i)hat(j)hat(k)]=[hat(j)hat(k)hat(i)]=[hat(k)hat(j)hat(i)]=1`
(ii)`[hat(i)hat(k)hat(j)]=[hat(k)hat(j)hat(i)]=[hat(j)hat(i)hat(k)]=1`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`[hat(i)hat(j)hat(k)]=(hat(i)xxhat(j)).hat(k)=hat(k).hat(k)=1`.
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RS AGGARWAL-PRODUCT OF THREE VECTORS-Objective Questions
  1. If vec(a) and vec(b) are mutually perpendicular unit vectors then (3ve...

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  2. If the vectors vec(a)=3hat(i)+hat(j)-2hatk and vec(b)=hat(i)+lambda ha...

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  3. If theta is the angle between two unit vectors hat(a) and hat(b) then ...

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  4. If vec(a)=(hat(i)-hat(j)+2hat(k)) and vec(b)=(2hat(i)+3hat(j)-4hat(k))...

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  5. If vec(a)=(hat(i)-2hat(j)+3hat(k)) and vec(b)=(hat(i)-3hat(k)) then |v...

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  6. If | vec a|=2,\ | vec b|=7\ a n d\ vec axx vec b=3 hat i+2 hat j+6 ha...

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  7. If |veca|=sqrt(26), |vecb|=7and| veca xx vecb|=35, then veca*vecb =

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

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  9. Find the area a parallelogram whose diagonals are vec a=3 hat i+ h...

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  10. Two adjacent sides of a triangle are represented by the vectors vec(a...

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  11. The unit vector normal to the plane containing vec(a)=(hat(i)-hat(j)-...

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  12. If vec a , vec b , and vec c are unit vectors such that vec a+ vec b...

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  13. If vec a ,\ vec b ,\ vec c are three mutually perpendicular unit ve...

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  14. Prove that (i) [hat(i)hat(j)hat(k)]=[hat(j)hat(k)hat(i)]=[hat(k)hat(...

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  15. Find the volume of the parallelepiped whose coterminous edges are r...

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  16. If the volume of a parallelepied having vec(a)=(5hat(i)-4hat(j)+hat(k)...

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  17. It is given that the vectorsvec(a)=(2hat(i)-2hat(k)), vec(b)=hat(i)+(l...

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  18. Which of the following is meaningless?

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  19. Prove that vecA.(vecAxxvecB)=0

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  20. For any three vectors vec a,vec b,vec c, (vec a-vec b)* (vec b-vec c)x...

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