CBSE Class 12-science Answered
Show that the line of intersection of the planes x+2y+3z=8 and 2x+3y+4z=11 is coplanar with the line x+1/1= y+1/3=z+1/3.also find the equation of the plane containing in them.
Asked by Vaspbrindha | 25 Dec, 2018, 10:44: PM
Expert Answer
Given Planes : x+2y+3z = 8 ..............(1)
2x + 3y + 4z = 11 ..............(2)
the plane passing through the intersection line of the planes (1) and (2) :- (x+2y+3z-8)+λ(2x+3y+4z-11) = 0 ...........(3)
where λ is constant
Equation of given line : 
.........................(4)
.........................(4)if the line given by eqn.(4) lies in the plane given by eqn.(3) then the points (-1,-1,-1) will be on the plane given in eqn.(3)
By substituiting coordinates of point (-1, -1, -1) on the plane given by eqn.(3), we can find λ as given below
(-1-2-3-8)+λ(-2-3-4-11) = 0 or λ = -7/10
By substituting λ in eqn.(3), we get the equation of plane that passing through the intersection of given planes
given by eqn.(1) and (2) as given below
4x+y-2z+3 = 0 ..................(5)
Direction ratios of normal to the plane givenm by eqn.(5) : a1 = 4 , b1 = 1, c1 = -2
Direction ratio of the line given by eqn.(4) :- a2 = 1 , b2 = 2, c3 = 3
a1a2 + b1b2 + c1c2 = 4+2-6 = 0 ................(6)
Eqn.(6) shows that given line that is given by eqn.(4) lies in the plane given by eqn.(5)
4x+y-2z+3 = 0 is the plane taht is passing through the intersection of planes given by eqn.(1) and (2) and has the line given by eqn.(4)
Answered by Thiyagarajan K | 28 Dec, 2018, 09:58: AM
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