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Let the pairs `a , b,and c ,d` each determine a plane. Then the planes are parallel if a.`( vec axx vec c)xx( vec bxx vec d)= vec0` b. `( vec axx vec c).( vec bxx vec d)= vec0` c. `( vec axx vec b)xx( vec cxx vec d)= vec0` d. `( vec axx vec b).( vec cxx vec d)= vec0`

A

`(vecaxxvecc)xx(vecbxxvecd)=vec0`

B

`(vecaxxvecc).(vecbxxvecd)=vec0`

C

`(vecaxxvecb)xx(veccxxvecd)=vec0`

D

`(vecaxxvecc).(veccxxvecd)=vec0`

Text Solution

Verified by Experts

The correct Answer is:
c
`veca xx vecb` is a vector perpendicular to the plane containing `veca and vecb` similarly, `vecc xx vecd` is a vector perpendicular to the plane containing , `vecc and vecd` thus , the two planes will be parallel if their normal i.e., `veca xx vecb and vecc xx vecd` are parallel. thus
`(veca xx vecb) xx (vecc xx vecd)) = vec0`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Two adjacent sides of a parallelogram A B C D are 2 hat i+4 hat j-5 ...

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  2. If hat a , hat b ,a n d hat c are three unit vectors inclined to ea...

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  3. Let the pairs a , b,and c ,d each determine a plane. Then the planes a...

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  4. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

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  5. If veca satisfies vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca is eq...

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  6. Vectors 3 vec a-5 vec b and 2 vec a+ vec b are mutually perpendicular....

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  7. The unit vector orthogonal to vector -hat i+ hat j+2 hat k and maki...

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  8. The value of x for which the angle between vec a=2x^2 hat i+4x hat ...

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  9. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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  10. A parallelogram is constructed on 2 vec a+ vec ba n d vec a-4 vec b...

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  11. Let vec adot vec b=0,w h e r e vec aa n d vec b are unit vectors and ...

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  12. If a \ a n d \ c are unit vectors and |b|=4 . The angel between aa n d...

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  13. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

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  14. A vector of magnitude sqrt(2) coplanar with the vector vec a= hat i+ ...

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  15. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

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  16. G is the centroid of triangle ABC and A1 and B1 are the midpoints of...

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  17. Points vec a , vec b , vec c ,a n d vec d are coplanar and (s inalpha...

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  18. If vec aa n d vec b are any two vectors of magnitudes 1 and 2, resp...

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  19. If vec a and vec b are any two vectors of magnitudes 2 and 3, respe...

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  20. veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4...

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