Home
Class 12
MATHS
The centre of the circle given by vec...

The centre of the circle given by ` vec r.( hat i+2 hat j+2 hat k)=15a n d| vec r.( hat j+2 hat k)|=4` is a. `(0,1,2)` b. `(1,3,4)` c. `(-1,3,4)` d. none of these

A

(0,1,2)

B

(1,3,4)

C

(-1,3,4)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
The equation of the line through the center `hatj+2hatj` and normal to the given plane is
`vecr=hatj=2hatk+lamda(hati+2hatj+2hatk)" "(i)`
This meets the plane for which
`[hatj+2hatk+lamda(hati+2hatj+2hatk)].(hati+2hatj+2hatk)=15`
or `6+9lamda=15orlamda=1`
Putting in (i), we get
`vecr=hatj+2hatk+(hati+2hatj+2hatk)=hati+3hatj+4hatk`
Hence, centre is (1,3,4).
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise REASONING TYPE|10 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise SUBJECTIVE TYPE|17 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

The angle between i and line of the intersection of the plane vec r . ( hat i+2 hat j+3 hat k)=0 and vec r . (3 hat i+3 hat j+ hat k)=0 is a. cos^(-1)(1/3) b. cos^(-1)(1/(sqrt(3))) c. cos^(-1)(2/(sqrt(3))) d. none of these

Find | vec axx vec b| , if vec a= hat i-7 hat j+7 hat k and vec b=3 hat i-2 hat j+2 hat kdot

A unit vector parallel to the intersection of the planes vec r. \ ( hat i- hat j+ hat k)=5 \ a n d \ vec r. \ (2 hat i+ hat j-3 hat k)=4 a. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) b. (-2 hat i+5 hat j-3 hat k)/(sqrt(38)) c. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) d. (-2 hat i-5 hat j-3 hat k)/(sqrt(38))

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

If vec (a) = 2 hat (i) - 3 hat (j) + 4 hat (k) and vec(b) = - 6 hat (i) + 9 hat (j) - 12 hat (k) , then

if vec a = 2 hat i- 3 hat j+hat k and vec b = hat i+2 hat j- 3hat k then vec aXvec b is

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r.( hat i- hat j+2 hat k)=5a n d vec r.(3 hat i+ hat j+ hat k)=6.

If vec (a)= 2 hat (i) - hat (j) + hat (k) and vec(b) = - hat (i) + 3 hat (j) + 4 hat (k) , then value of vec (a). vec(b) is -

CENGAGE PUBLICATION-THREE-DIMENSIONAL GEOMETRY -SINGLE CORRECT ANSWER TYPE
  1. The plane, which passes throught the point (3,2,0) and line (x - 3)/1 ...

    Text Solution

    |

  2. The direction ratios of a normal to the plane through (1,0,0)a n d(...

    Text Solution

    |

  3. The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15...

    Text Solution

    |

  4. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

    Text Solution

    |

  5. Distance of the point P( vec p) from the line vec r= vec a+lambda vec...

    Text Solution

    |

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

    Text Solution

    |

  7. The plane vec rdot vec n=q will contain the line vec r= vec a+lambda...

    Text Solution

    |

  8. The projection of point P( vec p) on the plane vec r. vec n=q is ( v...

    Text Solution

    |

  9. The angle between i and line of the intersection of the plane vec r ....

    Text Solution

    |

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

    Text Solution

    |

  11. The equation of the plane which passes through the line of intersect...

    Text Solution

    |

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

    Text Solution

    |

  13. Let vec a= hat i+ hat j and vec b=2 hat i- hat k , then the point of ...

    Text Solution

    |

  14. The coordinates of the point P on the line vec r=( hat i+ hat j+ h...

    Text Solution

    |

  15. The ratio in which the line segment joining the points whose positio...

    Text Solution

    |

  16. Find the following are equations for the plane passing through the p...

    Text Solution

    |

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

    Text Solution

    |

  18. L1a n dL2 and two lines whose vector equations are L1: vec r=lambda((c...

    Text Solution

    |

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

    Text Solution

    |

  20. The line through hati+3hatj+2hatk and perpendicular to the lines vecr=...

    Text Solution

    |