Home
Class 12
MATHS
The position vectors of points a and b a...

The position vectors of points a and b are `hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k)` respectively. The equation of plane is `rcdot(5hat(i)+2hat(j)-7hat(k))+9=0`. The points a and b

A

(a) lie on the plane

B

(b) are on the same side of the plane

C

(c) are on the opposite side of the plane

D

(d) None of these

Text Solution

Verified by Experts

The correct Answer is:
(c)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

If the position vectors of the point A and B are 3hat(i)+hat(j)+2hat(k) and hat(i)-2hat(j)-4hat(k) respectively. Then the eqaution of the plane through B and perpendicular to AB is

Show that the vectors 2hat(i)-hat(j)+hat(k) and hat(i)-3hat(j)-5hat(k) are at right angles.

Find the angle between the vectors a+b and a-b, if a=2hat(i)-hat(j)+3hat(k) and b=3hat(i)+hat(j)-2hat(k) .

Find the angle between the vectors hat(i)+3hat(j)+7hat(k) and 7hat(i)-hat(j)+8hat(k) .

The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-hat(j)+4hat(k)) and the plane rcdot(hat(i)+5hat(j)+hat(k))=5, is

A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(i)+hat(j)-hat(k) then the plane containing them is

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 7 hat i+ hat j- 3 hat k .

Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

Find the planes passing through the intersection of plane rcdot(2hat(i)-3hat(j)+4hat(k))=1 and rcdot(hat(i)-hat(j))+4=0 and perpendicular to planes rcdot(2hat(i)-hat(j)+hat(k))=-8

Find a unit vector perpendicular to the plane of two vectors a=hat(i)-hat(j)+2hat(k) and b=2hat(i)+3hat(j)-hat(k) .

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The equation of the plane perpendicular to the line (x-1)/(1), (y-2)/(...

    Text Solution

    |

  2. The locus of a point which moves so that the difference of the squares...

    Text Solution

    |

  3. The position vectors of points a and b are hat(i)-hat(j)+3hat(k) and 3...

    Text Solution

    |

  4. The vector equation of the plane through the point 2hat(i)-hat(j)-4hat...

    Text Solution

    |

  5. Let vector be the 2hat(i)+hat(j)-hat(k) then find the unit vector in ...

    Text Solution

    |

  6. For the line (x-1)/1=(y-2)/2=(z-3)/3, which one of the following is ...

    Text Solution

    |

  7. Find the value of m for which the straight line 3x-2y+z+3=0=4x-3y+4z+1...

    Text Solution

    |

  8. The length of projection of the line segment joining the points (1,0,-...

    Text Solution

    |

  9. The number of planes that are equidistant from four non-coplanar point...

    Text Solution

    |

  10. In a three-dimensional coordinate system, P ,Q ,and R are images of ...

    Text Solution

    |

  11. A plane passing through (1,1,1) cuts positive direction of coordinates...

    Text Solution

    |

  12. The equation of the line passing through (1, 1, 1) and perpendicular t...

    Text Solution

    |

  13. The equation of the plane through the intersection of the planes x+y+z...

    Text Solution

    |

  14. Two system of rectangular axes have the same origin. If a plane cuts t...

    Text Solution

    |

  15. ABC is an isosceles triangle right angled at A. forces of magnitude 2s...

    Text Solution

    |

  16. Consider the following 3lines in space L1:r=3hat(i)-hat(j)+hat(k)+la...

    Text Solution

    |

  17. Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+l...

    Text Solution

    |

  18. Find the shortest distance between the lines given by the equations ve...

    Text Solution

    |

  19. Find the angle between the line r=hat(i)+2hat(j)-hat(k)+lambda(hat(i)-...

    Text Solution

    |

  20. Consider three vectors p=i+j+k, q=2i+4j-k and r=i+j+3k. If p, q and r ...

    Text Solution

    |