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Two adjacent sides of a parallelogram ar...

Two adjacent sides of a parallelogram are respectively by the two vectors `hat(i)+2hat(j)+3hat(k)` and `3hat(i)-2hat(j)+hat(k)`. What is the area of parallelogram?

A

`8`

B

`8sqrt(3)`

C

`3 sqrt(8)`

D

`192`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(A) = i + 2j + 3k , vec(B) = 3i - 2j + k`
`vec(A) xx vec(B) = |(i , j , k), (1, 2, 3) , (3 , -2 , 1)| = 8 i - 8 j - 8k`
Area of parallelogram `= |vec(A) xx vec(B)| = 8 sqrt(3)`
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CP SINGH-VECTORS-Excercises
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  2. Which of the following vectors is//are perpendicular to the vector 4 I...

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  3. If vec(A) = 2 I + j - k , vec(B) = I + 2 j + 3 k , and vec(C ) = 6 i -...

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  4. Vectors which is perpendicular to ( a cos theta hat (i) + b sin theta ...

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  5. Two vectors vec A and vecB have equal magnitudes.If magnitude of (vecA...

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  6. The position vector of a particle is vec( r) = a cos omega t i + a sin...

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  7. The component of vector A= 2hat(i)+3hat(j) along the vector hat(i)+hat...

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  8. The vector component of vector vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k)...

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  9. If vec(A)xxvec(B)=vec(C ), then which of the following statements is w...

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  10. The magnitude of the vectors product of two vectors |vecA| and |vecB| ...

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  11. Three vector vec(A),vec(B), vec(C ) satisfy the relation vec(A)*vec(B)...

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  12. A vector vec(A) is along the positive x- axis . If B is another vector...

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  13. A vector vec(A) points verically upward and vec(B) points towards nort...

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  14. The value of (vec(A)+vec(B))xx(vec(A)-vec(B)) is

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  15. The scalar product of two vectors is 2 sqrt(3) and the magnitude of th...

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  16. If |vec(A)xxvec(B)|=sqrt(3)vec(A).vec(B), then the value of |vec(A)+ve...

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  17. The angle between the vector vec(A) and vec(B) is theta. Find the valu...

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  18. What is the unit vector perpendicular to the following vectors 2 hat(i...

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  19. Two adjacent sides of a parallelogram are respectively by the two vect...

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  20. The minimum number of vectors having different planes which can be add...

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