JEE Advance - Mathematics (2017 - Paper 2 Offline - No. 7)
The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y $$-$$ 2z = 5 and 3x $$-$$ 6y $$-$$ 2z = 7 is
14x + 2y $$-$$ 15z = 1
$$-$$14x + 2y + 15z = 3
14x $$-$$ 2y + 15z = 27
14x + 2y + 15z = 31
Explanation
Let the equation of plane be ax + by + cz = 1. Then
a + b + c = 1
2a + b $$-$$ 2c = 0
3a $$-$$ 6b $$-$$ 2c = 0
$$ \Rightarrow $$ a = 7b
c = $${{15b} \over 2}$$
b = $${{2} \over 31}$$, a = $${{14} \over 31}$$, c = $${{15} \over 31}$$
$$ \therefore $$ 14x + 2y + 15z = 31
a + b + c = 1
2a + b $$-$$ 2c = 0
3a $$-$$ 6b $$-$$ 2c = 0
$$ \Rightarrow $$ a = 7b
c = $${{15b} \over 2}$$
b = $${{2} \over 31}$$, a = $${{14} \over 31}$$, c = $${{15} \over 31}$$
$$ \therefore $$ 14x + 2y + 15z = 31
Comments (0)
