Find the point on the line of intersection of the two planes using Lagrange's method.

Use Lagrange's method to find the point on the line of intersection of the two planes $a_1x+a_2y+a_3z+a_0 = 0, b_1x+b_2y+b_3z+b_0 = 0$ which is nearest to the origin. you may also assume that the tow planes really intersect, but you should explain where this enters into the calculation.

I tried to solve this and I reached up to this point:

assuming $g=a_1x+a_2y+a_3z+a_0 = 0, h=b_1x+b_2y+b_3z+b_0 = 0$ and using Lagrange's multiplier method $L(x,y,z,\lambda,\mu) = f -\lambda g -\mu h$ and proceeding by taking the $gradient L =0$; I got the plane $2x^2+2y^2+2z^2 =0$. But the question need a point on the line of intersection of the two planes. How can I find this point?

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