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Multivariable CalculusHardLines & Planes in Space

Lines & Planes in Space · Hard problem

A point moves along the line r(t)=(1,0,0)+t⟨1,1,1⟩\mathbf r(t) = (1,0,0) + t\langle 1,1,1\rangle. Find the value of tt at which the point is equidistant from the two parallel planes 2x+y−2z=32x+y-2z=3 and 2x+y−2z=152x+y-2z=15.