Home
Class 12
MATHS
The equation of the plane which makes wi...

The equation of the plane which makes with coordinate axes, a triangle with its centroid `(alpha, beta , gamma)` is

A

`alpha x + beta y + gamma z=3`

B

`alpha x + beta y + gamma z = 1`

C

`(x)/( alpha )+ ( y)/( beta ) + (z)/( gamma)=1`

D

`(x)/( alpha)+( y)/( beta) + (z)/( gamma)=3`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS|42 Videos

  • SPECIMEN QUESTION PAPER

    ICSE|Exercise Section C|8 Videos

  • VECTORS

    ICSE|Exercise MULTIPLE CHOICE QUESTION |52 Videos

Similar Questions

Explore conceptually related problems

Find the equation of a plane which meets the axes in A ,Ba n dC , given that the centroid of the triangle A B C is the point (alpha,beta,gamma)

If alpha,beta,gamma be the angles which a line makes with the coordinates axes, then

If alpha, beta, gamma are the angles which a line makes with the coordinate axes ,then (A) sin^2alpha=cos^2beta+cos^2gamma (B) cos^2alpha+cos^2beta+cos^2gamma=2 (C) cos^2alpha+cos^2beta+cos^2gamma=1 (D) sin^2alpha+sin^2beta=1+cos^2gamma

The equation of plane parallel to the plane x+y+z=0 and passing through (alpha, beta, gamma0 is (A) x+y+z=alpha+beta+gamma (B) x+y+z=alphabeta+betagamma+gammaalpha (C) x+y+z+alpha+beta+gamma=0 (D) none of these

Let x-ysin alpha-zsin beta=0 , xsin alpha+zsin gamma-y=0 and xsin beta+ysin gamma-z=0 be the equations of the planes such that alpha+beta+gamma=pi//2 (where alpha,beta and gamma!=0)dot Then show that there is a common line of intersection of the three given planes.

If a line makes anles alpha, beta, gamma with the coordinate axes, porve that sin^2alpha+sin^2beta+sin^2gamma=2

If a plane meets the coordinates axes at A, Band C, in such a way that the centroid of Delta ABC is at the point (1,2,3) , the equation of the plane is

A variable plane is at constant distance 3 from origin and meets the axis in X,Y,Z planes through X,Y,Z parallel to coordinate planes are made. If P be the point of intersection of above made planes, given P(alpha, beta, gamma) then (alpha beta gamma)/(sqrt(alpha^(2)beta^(2)+beta^(2)gamma^(2)+gamma^(2)alpha^(2)))=?

If a line makes angles alpha, beta, gamma when the positive direction of coordinates axes, then write the value of sin^(2) alpha + sin^(2) beta + sin^(2) gamma .

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 then the coefficient of x in cubic equation whose roots are alpha ( beta + gamma ) , beta ( gamma + alpha) and gamma ( alpha + beta) is

ICSE-THREE DIMENSIONAL GEOMETRY-MULTIPLE CHOICE QUESTIONS
  1. If a line makes an angle of pi/4 with the positive directions of each ...

    Text Solution

    |

  2. If the planes x+2y+kz=5 and 2x +y-2z=0 are at right angles, then the v...

    Text Solution

    |

  3. The ratio in which the line segment joining the points (-2,4,5) and (3...

    Text Solution

    |

  4. The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to ...

    Text Solution

    |

  5. distance between the parallel planes ax+by+ cz + d =0 and ax+by + cz +...

    Text Solution

    |

  6. Equations of the line passing through (1,1,1) and perpendicular to th...

    Text Solution

    |

  7. The equation of the plane which makes with coordinate axes, a triangle...

    Text Solution

    |

  8. If a variable plane moves so that the sum of the reciprocals of its in...

    Text Solution

    |

  9. If angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane ...

    Text Solution

    |

  10. The angle between the lines 2x = 3 y=-z and 6x =-y= -4x is

    Text Solution

    |

  11. A vector parallel to the line of intersection of the planes overset(to...

    Text Solution

    |

  12. The locus represented by xy+yz=0 is

    Text Solution

    |

  13. If the planes overset(to)( r) (2 hat(i) - lambda (j) + 3 hat(k) ) = 0 ...

    Text Solution

    |

  14. The equation of the plane passing through the point (1, 1, 0) and perp...

    Text Solution

    |

  15. The distance of the point (2,1,-1) from the plane x-2y + 4z =9 is

    Text Solution

    |

  16. The angle between a line with direction ratios lt 2, 2, 1gt and a line...

    Text Solution

    |

  17. The lines (x-x1)/(a) = (y-y1)/(b) = (z-z1)/( c ) and (x-x1)/(a') = (y-...

    Text Solution

    |

  18. The vector equation of the line passing through the points A(3,4,-7) a...

    Text Solution

    |

  19. The vector equation of the line passing through the point (-1,5,4) and...

    Text Solution

    |

  20. The line (x-2)/(3) = (y-3)/(4)= (z-4)/(5) is parallel to the plane

    Text Solution

    |