# Sir,We know that whenever two planes intersect, they intersect in a line.How to find the equation of that line?Very urgent please reply soon

28 Points
14 years ago

Dear Anurag Kishore,

Ans:- Let the two planes be

A1x +B1y +C1z=D1................(1)

A2x+B2y+C2z=D2..................(2)

Now the Direction ratioes normal to the line

(1) are A1 B1 C1...........(3)

(2) are A2 B2 C2.........(4)

now by taking cross product of (3) & (4) we get the vector Q parallel to the required line.

Now the equation of the line is r=P+λQ

where We have got Q. But To find P i.e a point on the line let's consider point a,b,c which lie on the line and hence must satisfy both the equations (1) & (2) So,

A1a+B1b+C1c=D1............(5)

A2a+B2b+C2c=D2............(6)

Now eliminate one variable to make an equation of 2 variables say a & b.

Now by hit and trial method find one pair of a,b satisfying that equation then from it find c also.

So we now have one set of (a,b,c)

So we can find the line.

N.B:- The hit and trial method we have used because there will not be one and only fixed point on the line through which it is passing through.

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All the best Anurag Kishore !!!

Regards,