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Chapter: 12th Mathematics : UNIT 6 : Applications of Vector Algebra

Equation of line of intersection of two planes

Mathematics : Vector Algebra: Equation of line of intersection of two planes

Equation of line of intersection of two planes

Let   = p and   = q  be two non-parallel planes. We know that  and  are perpendicular to the given planes respectively.

So, the line of  intersection of these planes is perpendicular to both  × .    and  . Therefore, it is parallel to the vector  × . Let



Consider the equations of two planes a1x + b1y + c1z = p and a2x + b2y + c2z = q . The line of intersection of the two given planes intersects atleast one of the coordinate planes. For simplicity, we assume that the line meets the coordinate plane z = 0 . Substitute z=0 and obtain the two equations  a1x + b1y p = 0 and a2 x + b2y q = 0 .Then by solving these equations, we get the values of x and y as x1  and y1  respectively.

So,  ( x1 , y1 , 0) is a point on the required line, which is parallel to  l1iˆ + l2 ˆj + l3kˆ . So, the equation of the line is


 

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12th Mathematics : UNIT 6 : Applications of Vector Algebra


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