Equation of plane containing L1 and L2 is (a) x+y+z=0 (b) 3 x-2 y-z=0 (c) x-3 y+2 z=0 (d) x+y+z=

step 1 And the next question we need to find out the equation of plane underlying lines L1 and L2. So f

Equation of plane containing L1 and L2 is (a) x+y+z=0 (b) 3...

Key Concepts

Coplanarity of Lines

Coplanarity refers to the condition where two or more lines lie in the same plane. To determine if two lines are coplanar, one typically checks if there exists a plane whose equation is satisfied by points from both lines. This concept is central when finding a plane that contains multiple lines.

Cross Product to Determine a Normal Vector

The cross product of two non-parallel vectors lying in a plane yields a vector that is orthogonal to that plane. When two direction vectors, one from each line, are known, their cross product provides the normal vector required to construct the plane’s equation using the point-normal form.

Equation of a Plane in 3D

In three-dimensional geometry, a plane is commonly represented by an equation of the form Ax + By + Cz + D = 0, where (A, B, C) is a normal vector perpendicular to the plane. This formulation provides a systematic way to define a plane by specifying its orientation and how it is offset from the origin.

Direction Vectors and Parametric Representation of Lines

Lines in 3D are often expressed in parametric form, where each line is defined by a point on the line and a direction vector indicating its orientation. These direction vectors are crucial for understanding how lines lie in space and for determining if they are parallel, intersecting, or skew in relation to each other.

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