Questions
The equation of line parallel to the plane and intersecting the line at the point is
detailed solution
Correct option is C
The equation of plane is x+y−z+λ(x+2y−3z+5)=0It is passing through the point -4,1,3It implies that−4+1−3+λ(−4+2−9+5)=0⇒λ=−1Hence, the equation of plane is y−2z+5=0The required line is parallel to both planes y−2z+5=0 and x+y+z=2Normal vectors to above planes aren1=i+j+k,n2=j−2k The vector along the line is perpendicular to both the vectors, so it is along n1×n2Hence,n1×n2=ijk11101−2=−3i+2j+kHence, the direction ratios of the required line are ⟨−3,2,1⟩ Therefore, the equation of the required line is x+4−3=y−12=z−31Talk to our academic expert!
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