Home
Class 12
MATHS
From the point P(a ,b ,c), let perpendic...

From the point `P(a ,b ,c),` let perpendicualars `P La n dP M` be drawn to `Y O Za n dZ O X` planes, respectively. Then the equation of the plane `O L M` 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`

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`

Text Solution

Verified by Experts

The correct Answer is:
b
Coordinates of L and M are (0,b,c) and (a,0,c), respectively. Therefore, the equation of the plane passing through (0,0,0), (0,b,c) and (a,0,c) is
`|[x-0,y-0,z-0],[0,b,c],[a,0,c]|=0or(x)/(a)+(y)/(b)-(z)/(c)=0`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise REASONING TYPE|10 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise SUBJECTIVE TYPE|17 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Za n dZ X-p l a n e s find the vectors equation of the plane O A Bdot

If from a point P(a ,b ,c) prpendiculars P Aa n dP B are drawn to y za n dz x-p l a n e s , find the eqution of th plane O A Bdot

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

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0

Show that a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0 are perpendicular to x-y ,y-za n dz-x planes, respectively.

Show that a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0 are perpendicular to x-y ,y-za n dz-x planes, respectively.

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^(2)+b^2+c^2 d. a x+b y+c z=a+b+c

Find the equation of the plane containing the line (y)/(b)+(z)/(c)=1,x=0 , and parallel to the line (x)/(a)-(z)/(c)1,y=0 .

Find the reflection of the plane ax+by+cz+d=0 in the plane a\'x+b\'y+c\'z+d\'=0

CENGAGE ENGLISH-THREE-DIMENSIONAL GEOMETRY -SINGLE CORRECT ANSWER TYPE
  1. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c a...

    Text Solution

    |

  2. Distance of the point P(vecp) from the line vecr=veca+lamdavecb is ...

    Text Solution

    |

  3. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

    Text Solution

    |

  4. The plane vecr cdot vecn = q will contain the line vecr = veca + lambd...

    Text Solution

    |

  5. The projection of point P(vecp) on the plane vecr.vecn=q is (vecs), th...

    Text Solution

    |

  6. The angle between hati and line of the intersection of the plane vecr...

    Text Solution

    |

  7. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

    Text Solution

    |

  8. If vec a and vec b are two unit vectors and theta is the angle between...

    Text Solution

    |

  9. Consider triangle A O B in the x-y plane, where A-=(1,0,0),B-=(0,2,0)a...

    Text Solution

    |

  10. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

    Text Solution

    |

  11. The co-ordinates of the point P on the line vecr =(hati +hatj + hatk...

    Text Solution

    |

  12. The ratio in which the line segment joining the points whose position...

    Text Solution

    |

  13. Which of the following are equation for the plane passing through the ...

    Text Solution

    |

  14. Given vecalpha=3 hat i+ hat j+2 hat ka n d vecbeta= hat i-2 hat j-4 h...

    Text Solution

    |

  15. L(1)andL(2) are two lines whose vector equations are L(1):vecr=lamda...

    Text Solution

    |

  16. The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a...

    Text Solution

    |

  17. A long solenoid having n = 200 turns per metre has a circular cross-se...

    Text Solution

    |

  18. The line through of the plane passing through the lines (x-4)/(1)=(y-3...

    Text Solution

    |

  19. The three planes 4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10 a. meet in a poi...

    Text Solution

    |

  20. The equation of the plane through the line of intersection of the plan...

    Text Solution

    |