DeepCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.1 The Position Vector, #38 · Multivariable Calculus · Curves in space

Find the position vector to the shadow of … on the …

Find the position vector to the shadow of $t i + t^{2} j + t^{3} k$ on the $x z$ plane. Is the curve ever parallel to the line $x = y = z$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.1 The Position Vector, #38

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