Home
Class 12
MATHS
Find the equation of the line in vect...

Find the equation of the line in vector and in cartesian form that passes through the point with position vector `2 hat i- hat j+4 hat k` and is in the direction ` hat i+2 hat j- hat k` .

Text Solution

Verified by Experts

The correct Answer is:
`vec(r) = 2 hat(i) - hat(j) + 4 hat(k) + lambda ( hat(i) + 2 hat(j) - hat(k) ); `
`(x -2)/(1) = (y + 1)/(2) = (z -4)/(-1)` .
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise EXERCISE 11 (B) (LONG ANSWER TYPE QUESTIONS (I) )|10 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise EXERCISE 11 (B) (LONG ANSWER TYPE QUESTIONS (II) )|2 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise EXERCISE 11 (A) (LONG ANSWER TYPE QUESTIONS (II) )|2 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise CHAPTER TEST 10|12 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hat i-hat j+4hat k and is in the direction hat i+2hat j-hat k

Find the vector equation of a line which passes through the point with position vector 2hat i=hat j+4hat k and is in the direction of hat i+hat j-2hat k .Also,reduce it to Cartesian form.

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Find the Cartesian equation of a line which passes through the point having position vector (2hat(i) -hat(j) + 4hat(k)) and is in the direction of the vector , (hat(i) +2hat(j) -hat(k))

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

Find the vector equation of a plane passing through the point having position vector 2 hat(i) + hat(j) + hat(k) and perpendicular to the vector : 4 hat(i) - 2 hat(j) + 3hat(k) .

A unit vector perpendicular to the plane passing through the points whose position vectors are hat i-hat j+2hat k,2hat i-hat k and 2hat i+hat k is

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :

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

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -EXERCISE 11 (B) (SHORT ANSWER TYPE QUESTIONS )
  1. Show that the three lines with direction cosines (12)/(13),(-3)/(13),...

    Text Solution

    |

  2. Express the following equation of the lines into vector form : (x -...

    Text Solution

    |

  3. Find the cartesian as well as the vector equation of the line passing ...

    Text Solution

    |

  4. (A) The cartesian equations of a line are : (i) (x - 5)/(3) = (y + ...

    Text Solution

    |

  5. (A) find the equation of a line parallel to x-axis and passing through...

    Text Solution

    |

  6. (A ) Find the vector and cartesian equations of the line through the p...

    Text Solution

    |

  7. Find the equation of the line in vector and in cartesian form that ...

    Text Solution

    |

  8. Find the vector equation of the line passing thought the points (-1,\ ...

    Text Solution

    |

  9. Find the vector and cartesian equations of the line that passes throug...

    Text Solution

    |

  10. (A ) Find the equation of a st. line through (-1,2,3) and equally incl...

    Text Solution

    |

  11. Find the angle between the pairs of lines with direction-ratios : (...

    Text Solution

    |

  12. The angle between a line with direction ratios proportional to 2, 2, ...

    Text Solution

    |

  13. Find the angle between the following pairs of lines : (i) vec(r) = ...

    Text Solution

    |

  14. Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " a...

    Text Solution

    |

  15. (i) Find the value of 'p' so that the lines : l(1) : (1 - x)/(3) = (...

    Text Solution

    |

  16. Show that the line through the points : (a) (1, -1, 2), (3,4,-2) is ...

    Text Solution

    |