First slide

Planes in 3D

Question

If the equation of the plane passing through the line of intersection of the planes $a x + b y + c z + d = 0, a_{1} x + b_{1} y + c_{1} z + d_{1} = 0$ and perpendicular to the XY-plane is $p x + q y + r z + s = 0$ then S=

Moderate

A

$d c_{1} - d_{1} c$
B

$d c_{1} + d_{1} c$
C

$d d_{1} + c c_{1}$
D

$a a_{1} + b b_{1} + c c_{1}$

Solution

The plane equation is (ax + by + cz + d) - $(\frac{c}{c_{1}})$
$(a_{1} x + b_{1} y + c_{1} z + d_{1}) = 0$

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