Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Find the vector and Cartesian equations of the plane passing through the points(2, 2 –1), (3, 4, 2) and (7, 0, 6). Also find the vector equation of a plane passing through (4, 3, 1) and parallel to the plane obtained above.  

Find the vector and Cartesian equations of the plane passing through the points(2, 2 –1), (3, 4, 2) and (7, 0, 6). Also find the vector equation of a plane passing through (4, 3, 1) and parallel to the plane obtained above.

 

 

 

 
 
 
 
 

Answers (1)

Given: 

Let A(2,2,-1), B(3,4,2) & C(7,0,6)

The equation of plane passsing through A(2,2,-1)

a(x -2) +b(y -2) + c(z +1) = 0 \quad - (i)

\because (3,7,2) & (7,0,6) lie of the plane

        a + 2b + 3c = 0 \quad -(ii)

        5a - 2b + 7c = 0 \quad -(iii)

Solving equation (ii) and (iii), we get

    \frac{a}{14 + 6} = \frac{-b}{7-15} = \frac{c}{-2-10} = k \ (\text{assumption})

    \frac{a}{20} = \frac{-b}{-8} = \frac{c}{-12} = k

    putting the value of a, b and c in (i) we get

20k(x-2) + 8k(y-2)-12k(z + 1)=0 \\\Rightarrow 4k[5k-10 + 2y -4 -3z -3]= 0 \\\Rightarrow 5x +2y -3z - 17 = 0

This is the required equation of the plane.

Now, the second plane passes through the point (4,3,1)

\because this plane is parallel to the above plane,

\thereffore\therefore DR of the second plane be <5,2,-3>

So, the equation of the second plane

5(x-4) +2(y-3) -3(z-1) = 0 \\\Rightarrow 5x - 20 +2y -6 -3x + 3 =0 \\\Rightarrow 5x + 2y -3z -23 = 0

Posted by

Ravindra Pindel

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE admit card 2025 out for Class 10, 12 supplementary exams
anam-khan

CBSE Class 10, 12 practical exams 2025 for compartment students from July 10; detailed guidelines issued
anam-khan

CBSE Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in

Latest Question