The equation of the plane which passes through the line of intersection of the planes

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

The equation of the plane which passes through the line of intersection of the planes r⋅n1=q1r \cdot n_1 = q_1, r⋅n2=q2r \cdot n_2 = q_2 and is parallel to the line of intersection of the planes r⋅n3=q3r \cdot n_3 = q_3 and r⋅n4=q4r \cdot n_4 = q_4, is (1) [n2 n3 n4](r⋅n1−q1)=[n1 n3 n4](r⋅n2−q2)[n_2 \ n_3 \ n_4](r \cdot n_1 - q_1) = [n_1 \ n_3 \ n_4](r \cdot n_2 - q_2) (2) [n1 n2 n3](r⋅n4−q4)=[n4 n3 n1](r⋅n2−q2)[n_1 \ n_2 \ n_3](r \cdot n_4 - q_4) = [n_4 \ n_3 \ n_1](r \cdot n_2 - q_2) (3) [n4 n3 n1](r⋅n4−q4)=[n1 n2 n3](r⋅n2−q2)[n_4 \ n_3 \ n_1](r \cdot n_4 - q_4) = [n_1 \ n_2 \ n_3](r \cdot n_2 - q_2) (4) None of the above

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