Q. 135.0( 1 Vote )

Find the equation

Answer :

Given – A plane passes through points (1, 2, 3) and (0, - 1, 0) and is parallel to the line


To find – Equation of the plane


Tip – If a plane passes through points (a’, b’, c’), then its equation may be given as a(x - a’) + b(y - b’) + c(z - c’) = 0


Taking points (1, 2, 3):


a(x - 1) + b(y - 2) + c(z - 3) = 0…………(i)


The plane passes through (0, - 1, 0):


a(0 - 1) + b(- 1 - 2) + c(0 - 3) = 0


i.e. a + 3b + 3c = 0………………(ii)


The plane is parallel to the line


Tip – The normal of the plane will be normal to the given line since both the line and plane are parallel.


Direction ratios of the line is (2, 3, - 3)


Direction ratios of the normal of the plane is (a, b, c)


So, 2a + 3b - 3c = 0………………………(iii)


Solving equations (ii) and (iii),


[α → arbitrary constant]





Putting these values in equation (i) we get,






Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the equationMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the distanceMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the CartesiaMathematics - Board Papers

Find the coordinaMathematics - Board Papers