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Q.

Equation of the plane passing through the line of intersection of the two planes r→⋅n→1=q1 and r→⋅n→2=q2 and parallel to the line of intersection of r→⋅n→3=q3 and r→⋅n→4=q4 is

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a

dependent on n→1⋅n→3

b

dependent on n→3⋅n→4

c

independent of q1 and q2

d

independent of q3 and q4

answer is A.

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Detailed Solution

Equation of the required plane is r¯⋅n¯1−q1+λr¯⋅n¯2−q2=0⇒r¯⋅n¯1+λn2−=q1+λq2 Now, perpendicular to n¯3×n¯4⇒n¯1+λn¯2⋅n¯3×n¯4=0 So independent on q3 and q4 only.

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