Describe the curve defined by the vector functionr(t) = (4 + t, 1 + 3t,...

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Calculus

Describe the curve defined by the vector functionr(t) = (4 + t, 1 + 3t, -4 + 5t).SolutionThe corresponding parametric equations arex=_, y = 1 + 3t, z =which we recognize from the equationsx = xo + at, y = Yo + bt, z = Zo + ctas parametric equations of a line passing through the point (4, 1, -4) and parallel to the vector (1, 3, 5).Alternatively, we could observe that the function can be written as r = ro + tv, where ro = (4, 1, -4) and v =_____ and this is the vector equation of a line as given by the equation r=ro + tv.

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Describe the curve defined by the vector functionr(t) = (4 + t, 1 + 3t, -4 + 5t).SolutionThe corresponding parametric equations arex=___, y = 1 + 3t, z =____which we recognize from the equationsx = xo + at, y = Yo + bt, z = Zo + ctas parametric equations of a line passing through the point (4, 1, -4) and parallel to the vector (1, 3, 5).Alternatively, we could observe that the function can be written as r = ro + tv, where ro = (4, 1, -4) and v =_______ and this is the vector equation of a line as given by the equation r=ro + tv.