Q. 124.7( 3 Votes )

Find the coordinates of the point where the line intersect the plane x – y + z – 5 = 0. Also, find the angle between the line and the plane.[CBSE 2013]

Answer :

Any point on the line is of the form,

(3k + 2, 4k – 1, 2k + 2)


If the point p(3k + 2, 4k – 1, 2k + 2) lies in the plane x – y + z – 5 = 0, we have,


(3k + 2) – (4k – 1) + (2k + 2) – 5 = 0


3k + 2 – 4k + 1 + 2k + 2 – 5 = 0


k = 0


thus, the coordinates of the point of intersection of the line and the plane are :


{3(0) + 2, 4(0) – 1, 2(0) + 2}


P(2, – 1,, 2)


Let be the angle between the line and the plane . thus


, where l, m and n are the direction ratios of the line and a, b and c are the direction ratios of the normal to the plane


Here, l = 3, m = 4, n = 2, a = 1, b = – 1, and c = 1 hence,




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 GeometryQuestions Based on 3D GeometryQuestions Based on 3D Geometry26 mins
Questions Based on 3D Geometry | Check YourselfQuestions Based on 3D Geometry | Check YourselfQuestions Based on 3D Geometry | Check Yourself40 mins
Revision of straight lines important formulas in one shotRevision of straight lines important formulas in one shotRevision of straight lines important formulas in one shot59 mins
Concept Builder Questions of straight Lines (Quiz Session)Concept Builder Questions of straight Lines (Quiz Session)Concept Builder Questions of straight Lines (Quiz Session)55 mins
Reminding 11th - Revision of Circles important formulas in 50 MinutesReminding 11th - Revision of Circles important formulas in 50 MinutesReminding 11th - Revision of Circles important formulas in 50 Minutes56 mins
Conic Section Part 1Conic Section Part 1Conic Section Part 164 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
caricature
view all courses