Suppose a particle moves in the plane according to the vector-valued function $\mathbf { r } ( t ) = 2 e ^ { t } \mathbf { i } + e ^ { - t } \mathbf { j }$ , where t represents time. Find $\mathbf { v } ( t ) , | \mathbf { v } ( t ) | , \text { and } \mathbf { a } ( t )$ , and sketch a graph showing the path taken by the particle indicating the direction of motion.

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The Answer of Suppose a particle moves in the plane according to the vector-valued function $\mathbf { r } ( t ) = 2 e ^ { t } \mathbf { i } + e ^ { - t } \mathbf { j }$ , where t represents time. Find $\mathbf { v } ( t ) , | \mathbf { v } ( t ) | , \text { and } \mathbf { a } ( t )$ , and sketch a graph showing the path taken by the particle indicating the direction of motion.

Suppose a Particle Moves in the Plane According to the Vector-Valued