The equation of the plane which passes through the line of intersection of planes →r⋅→n1=q1,→r⋅→n2=q2 and is parallel to the line of intersection of planes →r⋅→n3=q3 and →r⋅→n4=q4 is
A
[→n2→n3→n4](→r⋅→n1−q1)=[→n1→n3→n4](→r⋅→n2−q2)
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B
[→n1→n2→n3](→r⋅→n4−q4)=[→n4→n3→n1](→r⋅→n2−q2)
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C
[→n4→n2→n1](→r⋅→n4−q4)=[→n1→n2→n3](→r⋅→n2−q2)
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D
None of these
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Solution
The correct option is A[→n2→n3→n4](→r⋅→n1−q1)=[→n1→n3→n4](→r⋅→n2−q2) The equation of the plane which passes through the line of intersection of planes →r⋅→n1=q1 and →r⋅→n2=q2 is
P:→r⋅→n1−q1+k(→r⋅→n2−q2)=0
Where k is real ⇒→r⋅(→n1+k⋅→n2)−q1−kq2=0 Since, P is parallel to the line of intersection of planes,
→r⋅→n3=q3 and →r⋅→n4=q4 Therefore, (→n1+k⋅→n2).(→n3×→n4)=0