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Find the equation of the straight line passing through the point( 1, 2, 3 )to intersect the straight line X + 1 = 2(y-2)=z+4 and parallel to the plane X + 5 y + 4 z = 0

Find the equation of the straight line passing through the point( 1, 2, 3 )to intersect the straight line X + 1 = 2(y-2)=z+4 and parallel to the plane X + 5 y + 4 z = 0

Grade:12

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
to fine the vector parellel to the line do cross product of the normal vector to the plane and made one more vector by using given point and one point from the given line
Rajat
213 Points
5 years ago
Let the point of intersection be,
(k-1, k/2+2, k-4)
Show the direction ratio of the required line=
(k-1-1, k/2+2-2, k-3-4) = (k-2, k/2, k-7)
 
The direction ratio of the normal to the given plane = ( 1, 5, 4)
the normal to the given plane is perpendicular to the required line since the required line is parallel to the given plane.
So, (1)(k-2)+(5)(k/2)+(4)(k-7) = k-2+5k/2+4k-28=15k/2-30=0 ; So, k = 4
The point of intersection is ( 3, 4, 0)
Eqn of the line is ;
(x-1)/(3-1)=(y-2)/(4-2)=(z-3)/(0-3)
Or, (x-1)/2= (y-2)/2 = (z-3)/(-3)

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