DeepCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.1 The Position Vector, #37 · Multivariable Calculus · Curves in space

True (with reason) or false (with example): (a) If … for all…

True (with reason) or false (with example):
(a) If $∣ R ∣ = 1$ for all $t$ then $∣ v ∣ =$ constant.
(b) If $a = 0$ then $R =$ constant.
(c) If $v \cdot v =$ constant then $v \cdot a = 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.1 The Position Vector, #37

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