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

question 53

Multiple Choice

Find $\mathbf { r } ( t )$ satisfying the conditions for $\mathbf { r } ^ { \prime } ( t ) = 6 e ^ { 6 t } \mathbf { i } + 7 e ^ { - t } \mathbf { j } + e ^ { t } \mathbf { k } , \quad \mathbf { r } ( 0 ) = \mathbf { i } - \mathbf { j } + 5 \mathbf { k }$

• A) \(6 e ^ { 6 t } \mathbf { i } - \left( 7 e ^ { - t } + 6 \right) \mathbf { j } + \left( e ^ { t } + 4 \right) \mathbf { k }\)
• B) \(e ^ { 6 t } \mathbf { i } - \left( 7 e ^ { - t } - 6 \right) \mathbf { j } + \left( e ^ { t } + 4 \right) \mathbf { k }\)
• C) \(\left( 6 e ^ { 6 t } + 1 \right) \mathbf { i } - \left( 7 e ^ { - t } - 1 \right) \mathbf { j } + \left( e ^ { t } + 5 \right) \mathbf { k }\)
• D) \(\left( e ^ { 6 t } + 1 \right) \mathbf { i } - \left( 7 e ^ { - t } + 1 \right) \mathbf { j } + \left( e ^ { t } + 5 \right) \mathbf { k }\)

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