Find the value of for which the plane touches the sphere .

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

Find the value of λ\lambda for which the plane x+y+z=3λx + y + z = \sqrt{3}\lambda touches the sphere x2+y2+z2−2x−2y−2z=6x^2 + y^2 + z^2 - 2x - 2y - 2z = 6 .

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