Home
Class 12
MATHS
Find the vector equation of a line which...

Find the vector equation of a line which passes through the point with position vector `hat(i)-2hat(j)+4hat(k)` and is in the direction of `hat(i)+2hat(j)-hat(k)`. Also, reduce it to cartesian from.

Text Solution

Verified by Experts

The correct Answer is:
`(x-1)/(1)=(y+2)/(2)=(z-4)/(-1)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Exercise 4A|81 Videos

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 Videos

  • SIGNIFICANCE OF DERIVATIVE AS RATE OF CHANGE

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITVE EXAMINATION|20 Videos

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

A line passes through the point with position vector 2 hat i-3 hat j+4 hat k and is in the direction of 3 hat i+4 hat j-5 hat kdot Find the equations of the line in vector and Cartesian forms.

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3hat(i)+2hat(j)-8hat(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.

Show that the poins whose position vectors are 4hat(i)+5hat(k),hat(i)+hat(j)+3hat(k)" and "-5hat(i)+3hat(j)-hat(k) are collinear.

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

If the points having position vectors hat(i)+bhat(j)+chat(k), 7hat(i)+2hat(j)+6hat(k) " and " 5hat(i)+2hat(j)+5hat(k) are collinear, find the values of b and c.

Find the equation in vector form of a line which is parallel to the vector hat(i)-2hat(j)+3hat(k) and which passes through the point (1,-2,5). Reduce it to cartesian form.

CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Sample Questions for Competitive Examination
  1. Find the vector equation of a line which passes through the point with...

    Text Solution

    |

  2. The symmetrical from of the lines x+y+z-1=0 and 4x+y-2z+2=0 are -

    Text Solution

    |

  3. The equation of line passing through the point vec(a) parallel to the ...

    Text Solution

    |

  4. The lines vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j)) and vec(r)...

    Text Solution

    |

  5. Consider the lines (x-5)/(3)=(y-7)/(-16)=(z-3)/(7) and (x-9)/(3)=(y-13...

    Text Solution

    |

  6. The distance of the point A(veca) from the line vec(r)=vec(b)+tvec(c)...

    Text Solution

    |

  7. If the length of the perpendicular drawn from (1,2,3) to the line (x-6...

    Text Solution

    |

  8. If the shortest distance between the lines (x-1)/(1)=(y-1)/(1)=(z-1)/(...

    Text Solution

    |

  9. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy xy=c^(...

    Text Solution

    |

  10. A line passing through the point (1,1,1) from a tiangle of area sqrt(6...

    Text Solution

    |

  11. The direction cosines of two lines satisfy the relations lamda(l+m)=n ...

    Text Solution

    |

  12. Each question in this section contains statements given in two columns...

    Text Solution

    |

  13. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

    Text Solution

    |

  14. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

    Text Solution

    |

  15. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

    Text Solution

    |

  16. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

    Text Solution

    |

  17. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

    Text Solution

    |

  18. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

    Text Solution

    |

  19. Statement - I: The point A (1,0,7) is the mirror image of the point B(...

    Text Solution

    |

  20. Statement - I : The lines vec(r)=hat(i)+hat(j)-hat(k)+S(3hat(i)-hat(j)...

    Text Solution

    |