Straight LineHard
Question
Equation of the plane containing the straight line 
and perpendicular to the plane containing the straight lines 
and 
is
and perpendicular to the plane containing the straight lines and is Options
A.x - 2y + 2z + 5 = 0
B.3x + 2y - 2z = 0
C.x - 2y + z = 0
D.5x + 2y - 4z = 0
Solution
Plane 1: ax + by + cz = 0 contains line
∴ 2a + 3b + 4c = 0 ......(i)
Plane 2: a′x + b′y + c′z = 0 is perpendicular to plane containing lines
and 
∴ 3a′ + 4b′ + 2c′ = 0 and 4a′ + 2b′ + 3c′ = 0
⇒
⇒ 8a - b - 10c = 0 .......(ii)
From (i) and (ii)
⇒ Equation of plane x - 2y + z = 0.
∴ 2a + 3b + 4c = 0 ......(i)
Plane 2: a′x + b′y + c′z = 0 is perpendicular to plane containing lines
and ∴ 3a′ + 4b′ + 2c′ = 0 and 4a′ + 2b′ + 3c′ = 0
⇒
⇒ 8a - b - 10c = 0 .......(ii)
From (i) and (ii)
⇒ Equation of plane x - 2y + z = 0.
Create a free account to view solution
View Solution FreeMore Straight Line Questions
The number of lines that are parallel to 2x + 6y − 7 = 0 and have an intercept 10 between the co-ordinate axis is...Tangents are drawn to the hyperbola , parallel to the straight line 2x - y = 1. The points ofcontact of the tangents on ...Let P = (-1,0),Q = (0, 0) and R = (3, 3√3) br three points. Then, the equations of the bisector of the angle PQR i...If the slope of a line is 2 and it cuts an intercept − 4 on y-axis, then its equation will be -...The line bx + ay = 3ab cuts the coordinate axes at A and B, then centroid of ᐃOAB is -...