Home
Class 12
MATHS
Let the pair of vector veca,vecb and vec...

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

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`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercises|15 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

Similar Questions

Explore conceptually related problems

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

Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(veccxxvecd)=vec0 . Let P_1 and P_2 be planes determined by pairs of vectors veca,vecb and vecc,vecd respectively. Then the angle between P_1 and P_2 is (A) 0 (B) pi/4 (C) pi/3 (D) pi/2

If veca,vecb,vecc are three non zero vectors (no two of which are collinear) such that the pairs of vectors (veca+vecb,vecc) and (vecb+vecc,veca) are colliner, then what is the value of veca+vecb+vecc ? (A) veca is parrallel to vecb (B) vecb (C) vecc (D) vec0

The vertices of a triangle have the position vectors veca,vecb,vecc and p( r) is a point in the plane of Delta such that: veca.vecb+ vecc.vecr = veca.vecc + vecb.vecr = vecb.vecc+veca.vecr then for the Delta , P is the:

Let veca, vecb and vecc be three vectors such that |veca|=2, |vecb|=1 and |vecc|=3. If the projection of vecb along veca is double of the projection of vecc along veca and vecb, vecc are perpendicular to each other, then the value of (|veca-vecb+2vecc|^(2))/(2) is equal to

If veca, vecb, vecc non-zero vectors such that veca is perpendicular to vecb and vecc and |veca|=1, |vecb|=2, |vecc|=1, vecb.vecc=1 . There is a non-zero vector coplanar with veca+vecb and 2vecb-vecc and vecd.veca=1 , then the minimum value of |vecd| is

If veca,vecb and vecc are three vectors of which every pair is non colinear. If the vector veca+vecb and vecb+vecc are collinear with the vector vecc and veca respectively then which one of the following is correct? (A) veca+vecb+vecc is a nul vector (B) veca+vecb+vecc is a unit vector (C) veca+vecb+vecc is a vector of magnitude 2 units (D) veca+vecb+vecc is a vector of magnitude 3 units

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2 then (A) veca,vecb,vecc are non coplanar (B) vecb,vecc, vecd are non coplanar (C) vecb, vecd are non paralel (D) veca, vecd are paralel and vecb, vecc are parallel

Let veca, vecb and vecc are three unit vectors in a plane such that they are equally inclined to each other, then the value of (veca xx vecb).(vecb xx vecc) + (vecb xx vecc). (vecc xx veca)+(vecc xx veca). (veca xx vecb) can be

If veca, vecb and vecc are three units vectors equally inclined to each other at an angle alpha . Then the angle between veca and plane of vecb and vecc is

CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Two adjacent sides of a parallelogram ABCD are 2hati+4hatj -5 hatkand ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. the unit vector orthogonal to vector -hati+2hatj+2hatk and making equa...

    Text Solution

    |

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

    Text Solution

    |

  9. If vectors veca and vecb are two adjecent sides of a paralleogram, the...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |