Q. 23

Find the vector equation of the plane passing through three points with position vectors and Also, find the coordinates of the point of intersection of this plane and the line [CBSE 2013]

Answer :

Let A, B and C be three point with position vector and

Thus,



As we know that cross product of two vectors gives a perpendicular vector so




So, the equation of the required plane is






Also we have to find the coordinates of the point of intersection of this plane and the line


Any point on the line is of the form, p(3 + 2, – 1 – 2, – 1 + )


Point p(3 + 2, – 1 – 2, – 1 + ) lies in the plane,


so,


9(3 + 2) – 3(– 1 – 2) – (– 1 + ) = 14


27 + 18 – 3 – 6 + 1 – = 14


11 = – 11


= – 1


Thus the required point of intersection is


p(3 + 2, – 1 – 2, – 1 + )


put value of in this equation


p[3 + 2(– 1), – 1 – 2(– 1), – 1 + (– 1)]


p(1, 1, – 2)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Questions Based on 3D Geometry26 mins
Revision of straight lines important formulas in one shot59 mins
Conic Section Part 164 mins
Reminding 11th - Revision of Circles important formulas in 50 Minutes56 mins
Concept Builder Questions of straight Lines (Quiz Session)55 mins
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
view all courses