Question
The equation of the plane which passes through the line of intersection of planes r⃗ .n⃗ 1=q1,r⃗ .n⃗ 2=q And is parallel to the line of intersection of planes r⃗ .n⃗ 3=q3 and r⃗ .n⃗ 4=q4is
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[a] (r⃗ .n⃗ 1+λr⃗ .n⃗ 2=q1+λq2) ??(i) Where λ is a parameter? So, n⃗ 1+λn⃗ 2 is normal to plane (i), now, any plane parallel to the line of intersection of the planes r⃗ .n⃗ 3=q3 and r⃗ .n⃗ 4=q4 is of the form r⃗ .(n⃗ 3×n⃗ 4)=d. Hence, we must have [n⃗ 1+λn⃗ 2].[n⃗ 3×n⃗ 4]=0 or [n⃗ 1n⃗ 3n⃗ 4]+λ[n⃗ 2n⃗ 3n⃗ 4]=0 or λ=−[n⃗ 1n⃗ 3n⃗ 4][n⃗ 2n⃗ 3n⃗ 4] on putting this value in Eq. (i), we have the equation of the required plane as r⃗ .n⃗ 1−q1=[n⃗ 1n⃗ 2n⃗ 4][n⃗ 2n⃗ 3n⃗ 4](r.n⃗ 2−q2) or [n⃗ 2n⃗ 3n⃗ 4](r⃗ .n⃗ 1−q1)=[n⃗ 1n⃗ 3n⃗ 4](r⃗ .n⃗ 2−q2)
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Question Text | The equation of the plane which passes through the line of intersection of planes r⃗ .n⃗ 1=q1,r⃗ .n⃗ 2=q And is parallel to the line of intersection of planes r⃗ .n⃗ 3=q3 and r⃗ .n⃗ 4=q4is |
Answer Type | Text solution:1 |
Upvotes | 150 |