Home
Class 12
MATHS
If the foot of the perpendicular from...

If the foot of the perpendicular from the origin to plane is `P(a ,b ,c)` , the equation of the plane is a. `x/a=y/b=z/c=3` b. `a x+b y+c z=3` c. `a x+b y+c z=a^(I2)+b^2+c^2` d. `a x+b y+c z=a+b+c`

A

`(x)/(a)+(y)/(b)+(z)/(c )=1`

B

`ax+by+cz=1`

C

`ax+by+cz=a^(2)+b^(2)+c^(2)`

D

`ax+by+cz=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTIONS))|16 Videos

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (NUMERICAL ANSWER TYPE QUESTIONS)|20 Videos

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (CONCEPT-BASED (SINGLE CORRECT ANSWER TYPE QUESTIONS ))|15 Videos

  • STATISTICS

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|13 Videos

  • TRIGONOMETRICAL IDENTITIES AND EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

If the foot of the perpendicular from the origin to plane is P(a,b,c), the equation of the plane is a.(x)/(a)=(y)/(b)=(z)/(c)=3bax+by+cz=3cax+by+cz=a^(2)+b^(2)+c^(2)dax+by+cz=a+b+c

If the foot of perpendicular from the point (1,-5,-10) to the plane x-y+z=5 is (a,b,c) then a+b+c=

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

P is a point (a,b,c). Let A,B,C be images of pin y-z,z-x and x-y planes respectively,then the equation of the plane ABC is

Show that |a b c a+2x b+2y c+2z x y z|=0

From the point P(a,b,c), let perpendicualars PL and PM be drawn to YOZ and ZOX planes,respectively.Then the equation of the plane OLM is a.(x)/(a)+(y)/(b)+(z)/(c)=0 b.(x)/(a)+(y)/(b)-(z)/(c)=0 c.(x)/(a)-(y)/(b)-(z)/(c)=0 d.(x)/(a)-(y)/(b)+(z)/(c)=0

Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

If a^x = b^y = c^z and b/a = c/b then (2z)/(x + z) is equal to:

MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -EXERCISE (LEVEL 1 (SINGLE CORRECT ANSWER TYPE QUESTIONS))
  1. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

    Text Solution

    |

  2. Equation of a plane bisecting an angle between the plane r.(i+2j+2k)=1...

    Text Solution

    |

  3. If the line (x-1)/(2)=(y-3)/(a)=(z+1)/(3) lies in the plane bx+2y+3z-4...

    Text Solution

    |

  4. Equation of the plane passing through the points i+j-2k,2i-j+kandi+2j+...

    Text Solution

    |

  5. The line of shortest distance between the lines (x-1)/(2)=(y+8)/(-7)...

    Text Solution

    |

  6. If r.n=q is the equation of a plane normal to the vector n, the length...

    Text Solution

    |

  7. If the foot of the perpendicular from the origin to plane is P(a ,b...

    Text Solution

    |

  8. The plane passing through the point (-2,-2, 2) and containing the line...

    Text Solution

    |

  9. Equation of a line passing through the point whose position vector is ...

    Text Solution

    |

  10. The lines r=i-j+lambda(2i+k) and r=2i-j+mu(i+j-k)

    Text Solution

    |

  11. The points (-2,5), (3, -4) and (7, 10) are the vertices of the triangl...

    Text Solution

    |

  12. The foot of the perpendicular from (a, b, c) on the line x=y=z is the ...

    Text Solution

    |

  13. Equation of a plane which passes through the line x+py+q=0=rz+s and ma...

    Text Solution

    |

  14. Parametric form of the equation of the line 3x-6y-2z-15=2x+y-2z-5=0 is

    Text Solution

    |

  15. A line with cosines proportional to 2,7-5 drawn to intersect the lines...

    Text Solution

    |

  16. The YZ-plane divides the line joining the points (3,5,-7)and(-2,1,8) i...

    Text Solution

    |

  17. Find the angle between the lines (x-2)/3=(y+1)/(-2)=z=2a n d(x-1)/1=(2...

    Text Solution

    |

  18. If the plane (x)/(a)+(y)/(b)+(y)/(c )=3 meets the coordinate axes in A...

    Text Solution

    |

  19. The variable plane (2lambda+1)x+(3-lambda)y+z=4 always passes through ...

    Text Solution

    |

  20. Algebraic sum of the intercepts by the plane 3x-4y+7z=84 on the axes i...

    Text Solution

    |