Home
Class 12
MATHS
The coordinates of the point P on the...

The coordinates of the point `P` on the line ` vec r=( hat i+ hat j+ hat k)+lambda(- hat i+ hat j- hat k)` which is nearest to the origin is a. `(2/4,4/3,2/3)` b. `(-2/3,-4/3,2/3)` c. `(2/3,-4/3,2/3)` d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find | vec a xx vec b|, if vec a=2 hat i+ hat j+3 hat k and vec b=3 hat i+5 hat j-2 hat k .

Find the angle between the line vec r = (2 hat i-hat j +3 hat k)+ lambda (3 hat i-hat j+2 hat k ) and the plane vec r.(hat i + hat j + hat k)=3

The distance of the line vec r=2 hat i-2 hat j+3 hat k+lambda( hat i- hat j+4 hat k) from the plane vec rdot(( hat i+5 hat j+ hat k))=5, is 5/(3sqrt(3)) b. (10)/(3sqrt(3)) c. (25)/(3sqrt(3)) d. none of these

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

Find the angle between the line -> r=(2 hat i+3 hat j+9 hat k)+lambda(2 hat i+3 hat j+4 hat k) and the plane -> r(dot( hat i+ hat j+ hat k))=5.

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. The ratio in which the line segment joining the points whose positi...

    Text Solution

    |

  5. The number of planes that are equidistant from four non-coplanar point...

    Text Solution

    |

  6. In a three-dimensional coordinate system, P ,Q , and Rare images of a...

    Text Solution

    |

  7. A plane passing through (1,1,1) cuts positive direction of coordinates...

    Text Solution

    |

  8. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

    Text Solution

    |

  9. The point of intersection of the line passing through (0,0,1) and ...

    Text Solution

    |

  10. Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-...

    Text Solution

    |

  11. Distance of point P( vec p) from the plane vec rdot vec n=0 is a. | v...

    Text Solution

    |

  12. The reflection of the point vec a in the plane vec rdot vec n=q ...

    Text Solution

    |

  13. Line vec r= vec a+lambda vec b will not meet the plane vec rdot vec ...

    Text Solution

    |

  14. If a line makes an angle of pi/4 with the positive direction of ea...

    Text Solution

    |

  15. A parallelepiped S has base points A ,B ,Ca n dD and upper face points...

    Text Solution

    |

  16. Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=...

    Text Solution

    |

  17. A plane which prependicular totwo planes 2x-2y+z=0and x-y+2z=4 passes ...

    Text Solution

    |

  18. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

    Text Solution

    |

  19. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersec...

    Text Solution

    |

  20. Consider a set of point R in which is at a distance of 2 units from t...

    Text Solution

    |