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Question

The equation of the plane which passes through the line of intersection of planes rn1=q1,rn2=q2 and is parallel to the line of intersection of planes rn3=q3 and rn4=q4 is

A
[n2 n3 n4](rn1q1)=[n1 n3 n4](rn2q2)
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B
[n1 n2 n3](rn4q4)=[n4 n3 n1](rn2q2)
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C
[n4 n2 n1](rn4q4)=[n1 n2 n3](rn2q2)
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D
None of these
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Solution

The correct option is A [n2 n3 n4](rn1q1)=[n1 n3 n4](rn2q2)
The equation of the plane which passes through the line of intersection of planes rn1=q1 and rn2=q2 is
P:rn1q1+k(rn2q2)=0
Where k is real
r(n1+kn2)q1kq2=0
Since, P is parallel to the line of intersection of planes,
rn3=q3 and rn4=q4
Therefore, (n1+kn2).(n3×n4)=0

k=n1.(n3×n4)n2.(n3×n4)=[n1 n3 n4][n2 n3 n4]
Substituting k in P, we get
[n2 n3 n4](rn1q1)=[n1 n3 n4](rn2q2)
Ans: A

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