Home
Class 12
MATHS
If the three planes rcdotn1=p1, rcdotn2=...

If the three planes `rcdotn_1=p_1, rcdotn_2=p_2 and rcdotn_3=p_3` have a common line of intersection, then `p_1(n_2timesn_3)+p_2(n_3timesn_1)+p_3(n_1timesn_2)` is equal to

A

`(1)/([n_1 n_2 n_3])[q_3(n_1timesn_2)+q_1(n_2timesn_3)+q_2(n_3timesn_1)]`

B

`(1)/([n_1 n_2 n_3])[q_1(n_1timesn_2)+q_1(n_2timesn_3)+q_3(n_3timesn_1)]`

C

`-(1)/([n_1 n_2 n_3])[q_1(n_1timesn_2)+q_1(n_2timesn_3)+q_3(n_3timesn_1)]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
(a)
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

Consider three planes P_1 : x-y + z = 1 , P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3 , P_3 and P_1 and P_1 and P_2 respectively. Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel . Statement 2:The three planes do not have a common point

If .^(n+5)P_(n+1)=.^(11(n-1))/2,^(n+3)P_(n) "then n is equal to" .

If the sum of n terms of an A.P is nP+1/2 n(n-1)Q , where P and Q are constant, find the common difference.

If the sum of n terms of an A.P. is given by delta_n=3n+2n^2 , then the common difference of an A.P. is

The line of greatest slope on an inclined plane P_1 is the line in the plane P_1 which is perpendicular to the line of intersection of the plane P_1 and a horizontal plane P_2 . Q. The coordinate of a point on the plane 2x+y-5z=0, 2sqrt(11) unit away from the line of intersection of 2x+y-5z=0 and 4x-3y+7z=0 are

If P_m stands for ""^mP_m , then : 1+1.P_1+2P_2+3P_3+.........+nP_n is equal to ,

Given planes P_1:cy+bz=x P_2:az+cx=y P_3:bx+ay=z P_1, P_2 and P_3 pass through one line, if

In R^3 , consider the planes: P_1: y=0 and P_2:x+z=1 . Let P_3 be a plane, different from P_1 and P_2 , which passes through the intersection of P_1 and P_2 . If the distance of the point (0,1,0) from P_3 is 1 and the distance of a point (alpha, beta, gamma) from P_3 is 2, then which of the following relations is (are) true?

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. A, B, C and D are four points in space. Using vector methods, prove th...

    Text Solution

    |

  2. Find the value of x Equation is x+2=9

    Text Solution

    |

  3. If the three planes rcdotn1=p1, rcdotn2=p2 and rcdotn3=p3 have a commo...

    Text Solution

    |

  4. A pentagon is formed by cutting a triangular corner from a rectangular...

    Text Solution

    |

  5. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

    Text Solution

    |

  6. A plane 2x+3y+5z=1 has a point P which is at minimum distance from lin...

    Text Solution

    |

  7. Evaluate int x^5 dx

    Text Solution

    |

  8. A cube C={(x, y, z)|o le x, y, zle1} is cut by a sharp knife along the...

    Text Solution

    |

  9. A ray of light is sent through the point P(1,2,3) and is reflected on ...

    Text Solution

    |

  10. Find dy/dx if 2x-3sinx=2y

    Text Solution

    |

  11. The shortest distance between any two opposite edges of the tetrahedro...

    Text Solution

    |

  12. The angle between the pair of planes represented by equation 2x^(2)-2y...

    Text Solution

    |

  13. Find the value of x Equation is x+1=1

    Text Solution

    |

  14. The four lines drawing from the vertices of any tetrahedron to the cen...

    Text Solution

    |

  15. The shorteast distance from (1, 1, 1) to the line of intersection of t...

    Text Solution

    |

  16. The shortest distance between the two lines L1:x=k1, y=k2 and L2: x=k3...

    Text Solution

    |

  17. A=[{:(l(1),m(1),n(1)),(l(2),m(2),n(2)),(l(3),m(3),n(3)):}] and B=[{:(p...

    Text Solution

    |

  18. ABCD is a tetrahedron such that each of the triangleABC, triangleABD a...

    Text Solution

    |

  19. What is 13% Equals to

    Text Solution

    |

  20. A variable plane makes intercepts on X, Y and Z-axes and it makes a t...

    Text Solution

    |