Find the Principal Unit Normal Vector N for the Curve $\mathbf { N } = ( - \sin t ) \mathbf { i } - ( \cos t ) \mathbf { k }$

question 59

Multiple Choice

Find the principal unit normal vector N for the curve r(t) .
-r(t) = (2t sin t + 2 cos t) i + (2t cos t - 2 sin t) ) k

• A) \(\mathbf { N } = ( - \sin t ) \mathbf { i } - ( \cos t ) \mathbf { k }\)
• B) \(\mathbf { N } = ( \cos t ) \mathbf { i } - ( \sin t ) \mathbf { k }\)
• C) \(\mathbf { N } = - \frac { \sqrt { 2 } } { 2 } ( \cos t ) \mathbf { i } - \frac { \sqrt { 2 } } { 2 } ( \sin t ) \mathbf { k }\)
• D) \(\mathbf { N } = ( \sin t ) \mathbf { i } + ( \cos t ) \mathbf { k }\)

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