Question
Question: If the axes are rectangular and P is the point (2, 3, –1), then the equation of the plane through ...
If the axes are rectangular and P is the point
(2, 3, –1), then the equation of the plane through P at right angles to OP, is –
A
2x + 3y + z = 14
B
2x + 3y – z = 14
C
2x – 3y + z = 14
D
None of these
Answer
2x + 3y – z = 14
Explanation
Solution
P is (2, 3, –1) and O is (0, 0, 0); direction cosines of OP
are proportional to (2, 3, –1).
Therefore these will be the coefficients of x, y, z in a plane which is perpendicular to OP.
So let the plane be 2x + 3y – z = l.
The plane also passes through P(2, 3, –1).
\ 4 + 9 + 1 = l
Ž l = 14.Hence the required plane is 2x + 3y – z = 14.