Home
Class 12
MATHS
If a vector vec(alpha) lies in the plane...

If a vector `vec(alpha)` lies in the plane of `vec(beta)andvec(gamma),` then

A

`[vecalpha, vecbeta, vecgamma]=1`

B

`[vecalpha, vecbeta, vecgamma]=1`

C

`[vecalpha, vecbeta, vecgamma]=0`

D

`[vecalpha, vecbeta, vecgamma]=2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Choose the correct answer)|31 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Answer the following questions)|21 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 6.9|8 Videos

  • APPLICATIONS OF MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (II. Answer the following)|15 Videos

  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Problem for practice|45 Videos

Similar Questions

Explore conceptually related problems

Let vec a = hat i + hat j + hat k, vec b = hat i - hat j + 2 hat k and vec c = x hat i +(x -2) hat j - hatk .If the vector vec c lies in the plane of veca and vecb , thenx equals

If vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=hat(i)+2hat(j)-5hat(k),vec(c)=3hat(i)+5hat(j)-hat(k), then a vector perpendicular to vec(a) and lies in the plane containing vec(b)andvec(c) is

If ( vec axx vec b)xx( vec cxx vec d)dot( vec axx vec d)=0 , then which of the following may be true? a. vec a , vec b , vec ca n d vec d are necessarily coplanar b. vec a lies in the plane of vec ca n d vec d c. vec b lies in the plane of vec aa n d vec d d. vec c lies in the plane of vec aa n d vec d

Let vec(a) and vec(b) be two unit vectors such that vec(a).vec(b)=0 For some x,y in R , let vec(c)=xvec(a)+yvec(b)+(vec(a)xxvec(b)) If |vec(c)|=2 and the vector vec(c) is inclined at same angle alpha to both vec(a) and vec(b) then the value of 8cos^2alpha is

If vector vec a+ vec b bisects the angle between vec a and vec b , then prove that | vec a| = | vec b| .

Let veca,vecb,vecc be three non-zero vectors such that vec(c) is a unit vector perpendicular to both vec(a)andvec(c). If the angle between vec(a)andvec(c)" is "(pi)/(6)," show that "[vec(a),vec(b),vec(c)]^(2)=(1)/(4)absvec(a)^(2)absvec(b)^(2).

vec u , vec va n d vec w are three non-coplanar unit vecrtors anf alpha,betaa n dgamma are the angles between vec ua n d vec v , vec va n d vec w ,a n d vec wa n d vec u , respectively, and vec x , vec ya n d vec z are unit vectors along the bisectors of the angles alpha,betaa n dgamma , respectively. Prove that [ vec xxx vec y vec yxx vec z vec zxx vec x]=1/(16)[ vec u vec v vec w]^2sec^2alpha/2sec^2beta/2sec^2gamma/2dot

If the vector product of a constant vector vec O A with a variable vector vec O B in a fixed plane O A B be a constant vector, then the locus of B is a. a straight line perpendicular to vec O A b. a circle with centre O and radius equal to | vec O A| c. a straight line parallel to vec O A d. none of these

PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-SOLUTION TO EXERCISE 6.10
  1. If veca and vecb are parallel vector, then [(veca,vecb,vecc)] is equal...

    Text Solution

    |

  2. If a vector vec(alpha) lies in the plane of vec(beta)andvec(gamma), th...

    Text Solution

    |

  3. If veca*vecb=vecb*vec c=vec c *veca=0, then the value of [veca, vecb, ...

    Text Solution

    |

  4. If vec(a),vec(b),vec(c) are three unit vectors such that vec(a) is per...

    Text Solution

    |

  5. If [veca, vecb, vec c]=1, then the value of (veca*(vecb xx vec c))/((v...

    Text Solution

    |

  6. The volume of the parallelepiped with its edges represented by the vec...

    Text Solution

    |

  7. If veca and vecb are unit vectors such that [veca, vecb, veca xx vecb]...

    Text Solution

    |

  8. If veca=hati+hatj+hatk,vecb=hati+hatj, vecc= veci and (vecaxxvec...

    Text Solution

    |

  9. If vec(a),vec(b),vec(c) are non-coplanar, non-zero vectors such that [...

    Text Solution

    |

  10. If vec(a),vec(b),vec(c) are three non-coplanar vectors such that vec(a...

    Text Solution

    |

  11. If the volume of the parallelpiped with vec(a)xxvec(b),vec(b)xxvec(c),...

    Text Solution

    |

  12. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

    Text Solution

    |

  13. If vec(a)xx(vec(b)xxvec(c))=(vec(a)xxvec(b))xxvec(c)," where "vec(a),v...

    Text Solution

    |

  14. If bara = 2hati + 3hatj - hatk, barb = hati + 2hatj - 5hatj, barc = 3h...

    Text Solution

    |

  15. The angle between the lines (x-2)/(3)=(y+1)/(-2),z=2and(x-1)/(1)=(2y+3...

    Text Solution

    |

  16. If the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2)" lies in the plane "x+3y-az...

    Text Solution

    |

  17. The angle between the line vecr=(hati+2hatj-3hatk)+t(2hati+hatj-2hatk)...

    Text Solution

    |

  18. The coordinates of the point where the line vecr=(6hati-hatj-3hatk)+t(...

    Text Solution

    |

  19. Distance from the origin to the plane 3x - 6y + 2z + 7 = 0 is

    Text Solution

    |

  20. The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z +...

    Text Solution

    |