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

Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to the plane `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

`vecr = (3hati - 5hatj + 7hatk)+lambda (3hati- 4hatj +5hatk)`

D

`vecr = (3hati - 4hatj -5hatk)+mu(3hati +5hatj +7hatk)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - D COMPREHENSION I|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - D COMPREHENSION II|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - B|47 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Section - J (Akash Challengers Question)|16 Videos

Similar Questions

Explore conceptually related problems

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.

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 the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x-5y-15=0. Also, show that the plane thus obtained contains the line vec r= hat i+3 hat j-2 hat k+lambda( 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 the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

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

Find the vector equation of the plane passing through the points (2,\ 1,\ -1)\ a n d\ (-1,\ 3,\ 4) and perpendicular to the plane x\ -\ 2y+4z=10 . Also show that the plane thus obtained contains the line vec r=- hat i+3 hat j+4 hat k+lambda\ (3 hat i-2 hat j-\ 5 hat k)dot

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

Find the vector and Cartesian equations of the line through the point (1, 2, 4) and perpendicular to the two lines vec r=(8 hat i-19 hat j+10 hat k)+lambda(3 hat i-16 hat j+7 hat k) and vec r=(15 hat i+29 hat j+5 hat k)+mu(3 hat i+8 hat j-5 hat k)dot

Find the equation of plane passing through the point hat i+ hat j+ hat k and parallel to the plane vecr.(2 hat i- hat j+2 hat k)=5.