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

question 73

Multiple Choice

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

• 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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Definitions:

Robbery

The unlawful taking or attempted taking of personal property by force or threat of force and/or by putting the victim in fear.

Explosive Device

A tool or weapon designed to explode, causing damage or destruction through the rapid release of energy.

Arson

The crime of intentionally setting fire to another’s property.

Intentional Destruction

The deliberate act of destroying or causing damage to property or materials.