Home
Class 12
MATHS
Let A = (1,1,-1) and B = (0, 2,1) be two...

Let A = (1,1,-1) and B = (0, 2,1) be two given points .Also, let P:x+y+z=0 be a plane. The equation of the line perpendicular to `vec(AB)` and lying completely in the plane 'P' is

A

(a) `(x-2/3)/1=(y-1/2)/(-3) = (z+2)/2`

B

(b) `(x-3)/2=(y-1)/-6=(z+2)/2`

C

(c) `x=y=z`

D

(d) `x-3=y-1=z=2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • EQUATION OF PLANE AND ITS APPLICATIONS -I

    CENGAGE|Exercise DPP 3.3|22 Videos

  • FUNCTIONS

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

Let A=(1,1,-1),B=(0,2,1) be two given points. Also, let P: x+y+z=0 be a plane. If A^(') and B^(') are the feet of perpendicular from A and B, respectively, on the plane 'P' then A^(')B^(') equals

The line (x)/(a)-(y)/(b) =1 cuts the x-axis at P. The equation of the line through P perpendicular to the given line is

Let P_(1):x+y+2z-3=0 and P_(2)=x-2y+z=4 be two planes. Also, let A(1,3,4) and B(3,2,7) be two points in space. The equation of plane which passes through line of intersection of P_(1) and P_(2) upon which length of projection of the line segment AB is the least, is

Let P_(1):x+y+2z-3=0 and P_(2)=x-2y+z=4 be two planes. Also, let A(1,3,4) and B(3,2,7) be two points in space. The equation of plane which passes through line of intersection of P_(1) and P_(2) and upon which length of projection of the line segment AB is the greatest, is

Find the equation of the plane perpendicular to the line (x-1)/2=(y-3)/(-1)=(z-4)/2 and passing through the origin.

Equation of line of projection of the line 3x-y+2z-1=0=x+2y-z=2 on the plane 3x+2y+z=0 is

Let the equations of a line and plane be (x+3)/2=(y-4)/3=(z+5)/2a n d4x-2y-z=1, respectively, then a. the line is parallel to the plane b. the line is perpendicular to the plane c. the line lies in the plane d. none of these

A variable point P is on the circle x^2 + y^2 =1 on xy plane. From point P, perpendicular PN is drawn to the line x =y =z then the minimum length of PN is:-

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

CENGAGE-EQUATION OF PLANE AND ITS APPLICATIONS -II-DPP 3.4
  1. Let A(0,6,6), B(6,6,0) and C(6,0,6) are three points and point D is mo...

    Text Solution

    |

  2. Equation of line of projection of the line 3x-y+2z-1=0=x+2y-z=2 on the...

    Text Solution

    |

  3. The orthocenter of triangle whose vertices are A(a,0,0),B(0,b,0) and C...

    Text Solution

    |

  4. The shortest distance between the lines 2x+y+z-1=0=3x+y+2z-2 and x=y=z...

    Text Solution

    |

  5. If plane 2x+3y+6z+k=0 is tangent to the sphere x^(2)+y^(2)+z^(2)+2x-2y...

    Text Solution

    |

  6. The shortest distance from (1,1,1) to the line of intersection of the ...

    Text Solution

    |

  7. A variable plane makes intercepts on x, y and z axes and it makes a te...

    Text Solution

    |

  8. If the projection of the line x/2=(y-1)/2=(z-1)/1 on a plane P is x/1=...

    Text Solution

    |

  9. Image of sphere x^(2)+y^(2)+z^(2)=9 in plane 2x+3y+4z-29=0 is

    Text Solution

    |

  10. The locus of point which moves in such a way that its distance from th...

    Text Solution

    |

  11. A plane cutting the axes in P,Q,R passes through (alpha,beta,beta-lamb...

    Text Solution

    |

  12. Let a plane pass through origin and be parallel to the line (x-1)/2=(y...

    Text Solution

    |

  13. The planes ax+4y+z=0,2y+3z-1=0 and 3x-bz+2=0 will

    Text Solution

    |

  14. If the line x/1=y/2=z/3 intersects the the line 3beta^(2)+3(1-2alpha)y...

    Text Solution

    |

  15. Let A=(1,1,-1),B=(0,2,1) be two given points. Also, let P:x+y+z=0 be a...

    Text Solution

    |

  16. Let A = (1,1,-1) and B = (0, 2,1) be two given points .Also, let P:x+y...

    Text Solution

    |

  17. Let P(1):x+y+2z-3=0 andP(2)=x-2y+z=4 be two planes. Also, let A(1,3,4)...

    Text Solution

    |

  18. Let P(1):x+y+2z-3=0 andP(2)=x-2y+z=4 be two planes. Also, let A(1,3,4)...

    Text Solution

    |