1. The number of points of intersection of the surface $z = x^2 + y^2$ with the line having parametric equations $x = 3 + t$, $y = -1 - t$, $z = -2 - 2t$, $t \in \mathbb{R}$ is: (a) zero; (b) infinite; (c) three; (d) two; (e) one. [2]
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Substituting x = 3 + t, y = -1 - t, and z = -2 - 2t into the equation z = y, we get: -2 - 2t = -1 - t Simplifying this equation, we get: t = -1 Now, let's substitute this value of t back into the equations of the line to find the corresponding values of x, y, Show more…
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