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Reparametrize the Curve with Respect to Arc Length Measured from the Point

Question 53

Multiple Choice

Reparametrize the curve with respect to arc length measured from the point where t=0t = 0 in the direction of increasing tt .
r(t) =(7+3t) i+(10+9t) j(6t) k\mathbf { r } ( t ) = ( 7 + 3 t ) \mathbf { i } + ( 10 + 9 t ) \mathbf { j } - ( 6 t ) \mathbf { k }


A) r(t(s) ) =(73126s) i+(10+9126s) j(6s126) k\mathbf { r } ( t ( s ) ) = \left( 7 - \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }
B) r(t(s) ) =(7+3126s) i+(109126s) j(6s126) k\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 - \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }
C)
r(t(s) ) =(7+3126s) i+(10+9126s) j(6s126) k\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }
D)
r(t(s) ) =(7+3126s) i+(10+9126s) j+(6s) k\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } + ( 6 s ) \mathbf { k }
E)
r(t(s) ) =(7+3126s) i+(10+9126s) j(6s) k\mathbf { r } ( t ( s ) ) = \left( 7 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 10 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - ( 6 s ) \mathbf { k }

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