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

Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to theplane `3x-4y+5z=8.`

A

`(x-3)/(3)=(y+5)/(-4)=(z-7)/(5)`

B

`(x-3)/(3)=(y+4)/(-5)=(z-5)/(7)`

C

`r=3i+5j-7k+lambda(3i-4j-5k)`

D

`r=3i-4j-5k+mu(3i+5j+7k)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS)|23 Videos
  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (CONCEPT-BASED (SINGLE CORRECT ANSWER TYPE QUESTIONS ))|15 Videos
  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 1( SINGLE CORRECT ANSWER TYPE QUESTIONS))|55 Videos
  • STATISTICS

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|13 Videos
  • TRIGONOMETRICAL IDENTITIES AND EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

Find the vector equation of a line passing through 3hat i-5hat j+7hat k and perpendicular to theplane 3x-4y+5z=8

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

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 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.

Find the vector equation of plane passing through the points 2hat i+hat j-hat k and -hat i+3hat j+4hat k and perpendicular to the plane vec r*(hat i-2hat j+4hat k)=10

Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane vec r*(hat i+2hat j-5hat k)+9=0

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

(i) Find the vector equation of a line passing through a point with position vector 2 hat(i) - hat(j) + hat(k) and parallel to the line joining the points with position vectors - hat(i) + 4 hat(j) + hat(k) and hat(i) + 2 hat(j) + 2 hat(k). Also, find the cartesian equivalent of the equation. (ii) Find the vector equation of a line passing through the point with position vector hat(i) - 2 hat(j) - 3 hat(k) and parallel to the line joining the points with position vectors hat(i) - hat(j) + 4 hat(k) and 2 hat(i) + hat(j) + 2 hat(k) . Also, find the cartesian form of the equation.

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

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) .

MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -SOLVED EXAMPLES (LEVEL 2( SINGLE CORRECT ANSWER TYPE QUESTIONS))
  1. A line segment has length 63 and direction ratios are 3, -26. The comp...

    Text Solution

    |

  2. Find the equations of the bisectors of the angles between the plane...

    Text Solution

    |

  3. Find the vector equation of a line passing through 3 hat i-5 hat j+...

    Text Solution

    |

  4. If the perpendicular distance of a point A, other than the origin from...

    Text Solution

    |

  5. If d(1),d(2),d(3) denote the distances of the plane 2x-3y+4z=0 from th...

    Text Solution

    |

  6. Equation of the plane containing the lines. r=i+2j-k+lambda(i+2j-k) ...

    Text Solution

    |

  7. Show that the foot of the perpendicular from the origin to the join of...

    Text Solution

    |

  8. Cosine of the angle between the lines whose vector equations are r=3i+...

    Text Solution

    |

  9. Find the equation of the plane through the line of intersection of ve...

    Text Solution

    |

  10. If 1,m ,n are the direction cosines of the line of shortest distance b...

    Text Solution

    |

  11. Equation of the line through the point (2,-1,1) and the intersection o...

    Text Solution

    |

  12. Under what condition do the planes bx-ay=n,cy-bz=l,az-cx=m intersect ...

    Text Solution

    |

  13. The value of k such that (x-4)/1=(y-2)/1=(z-k)/2 lies in the plane 2x-...

    Text Solution

    |

  14. A variable plane at distance of 1 unit from the origin cuts the coordi...

    Text Solution

    |

  15. A plane passes through (1,-2,1) and is perpendicualr to two planes 2x...

    Text Solution

    |

  16. A line with positive direction cosines passes through the point P(2, –...

    Text Solution

    |

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

    Text Solution

    |

  18. Equation of the plane containing the straight line x/2=y/3=z/4 and per...

    Text Solution

    |

  19. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  20. Read the following passage and answer the questions. Consider the line...

    Text Solution

    |