Study Room

Goto

Eamcet Mathematics
Co - ordinate Geometry 3D Geometry

Take Exam
Previous
72 / 91
Next

Q.

The equation of the plane through the points (2, 2, 1) and (1, –2, 3) and parallel to the line joining the points (3, 2, –2) and (0, 6, –7) is

View Answer

Correct choice: C

Explanation:

Any plane through (2, 2, 1) is a(x–2) + b(y –2) + c(z–1) = 0 ……………(1)
Since it passes through (1, –2, 3)
a(1 –2) + b(–2 –2) + c(3 –1) = 0
Or –a – 4b + 2c = 0 ……………(2)
d.r. of the parallel line is 3, –4, 5
As a, b, c is the d.r. of normal to the plane which is parallel to the line with d.r. 3, –4, 5
∴ 3a – 4b + 5c = 0 …………….(3)
On solving (2) & (3) we get a/12 =6/-11 = c/-16
∴ From (1), required equation is 12(x–2) –11(y –2) – 15(z–1) = 0
Previous
72 / 91
Next