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Let the pair of vector veca,vecb and vec...

Let the pair of vector `veca,vecb` and `vecc,veccd` each determine a plane. Then the planes are parallel if

A

`(vecaxxvecc)xx(vecbxxvecd)=vec0`

B

`(vecaxxvecc).(vecbxxvecd)=vec0`

C

`(vecaxxvecc)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-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Two adjacent sides of a parallelogram ABCD are 2hati+4hatj -5 hatkand ...

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  2. If hata,hatb and hatc are three unit vectors inclined to each other at...

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  3. Let the pair of vector veca,vecb and vecc,veccd each determine a plane...

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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 3veca-5vecb and 2veca + vecb are mutually perpendicular. If ve...

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  7. The units vectors orthogonal to the vector - hat i + 2hat j + 2hat k ...

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  8. The value of x for which the angle between veca = 2x^(2) hati + 4x h...

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  9. If vectors veca and vecb are two adjacent sides of parallelograsm then...

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  10. A parallelogram is constructed on 3veca+vecb and veca-4vecb, where |ve...

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  11. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

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  12. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

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

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  14. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

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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 s...

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  17. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

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  18. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

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  19. If veca and vecb are any two vectors of magnitude 2 and 3 respective...

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

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