Find $\mathbf { r } ( t )$ Satisfying the Conditions For

question 54

Multiple Choice

Find $\mathbf { r } ( t )$ satisfying the conditions for $\mathbf { r } ^ { t } ( t ) = 9 e ^ { 9 t } \mathbf { i } + 9 e ^ { - t } \mathbf { j } + e ^ { t } \mathbf { k }$ $\mathbf { r } ( 0 ) = \mathbf { i } - \mathbf { j } + 9 \mathbf { k }$

• A) \(\left( e ^ { 9 t } + 1 \right) \mathbf { i } - \left( 9 e ^ { - t } + 1 \right) \mathbf { j } + \left( e ^ { t } + 9 \right) \mathbf { k }\)
• B) \(9 e ^ { 9 t } \mathbf { i } - \left( 9 e ^ { - t } + 8 \right) \mathbf { j } + \left( e ^ { t } + 8 \right) \mathbf { k }\)
• C) \(e ^ { 9 t } \mathbf { i } - \left( 9 e ^ { - t } - 8 \right) \mathbf { j } + \left( e ^ { t } + 8 \right) \mathbf { k }\)
• D) \(\left( 9 e ^ { 9 t } + 1 \right) \mathbf { i } - \left( 9 e ^ { - t } - 1 \right) \mathbf { j } + \left( e ^ { t } + 9 \right) \mathbf { k }\)

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