About the line 
= 
= 
the plane 3x + 4y + 6z + 7 = 0 is rotated till the plane passes through the origin. Now 4x + α y + β z = 0 is the equation of plane in new position. The value of α 2 + β 2 is
Text Solution
Verified by Experts32
(32)
Sol. Since 3(2) + 4(–3) + 6(1) = 0 and 3(1) + 4(2) + 6(–3) + 7 = 0
∴ the line 
= 
= 
lies in the plane 3x + 4y + 6z + 7 = 0.
In the new position again the line lies in the plane. Let the equation of the new position of the plane be ax + by + cz = 0, then 2a – 3b + c = 0 and a + 2b – 3c = 0
∴ 
= 
= 
i.e. a = b = c
∴ equation of the required plane is x + y + z = 0
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems