Find T, N, and B for the given space curve.
-$$\mathbf { r } ( t ) = ( 8 + t ) \mathbf { i } + ( 9 + \ln ( \sec t ) ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2

Question

Find T, N, and B for the given space curve.
-$$\mathbf { r } ( t ) = ( 8 + t ) \mathbf { i } + ( 9 + \ln ( \sec t ) ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2 < t < \pi / 2$$
A) T = (-cos t)i - (sin t)j; N = (sin t)i - (cos t)j ; B = -k
B) T = (cos t)i + (sin t)j; N = (- sin t)i + (cos t)j ; B = k
C) T = (cos t)i - (sin t)j; N = (-sin t)i - (cos t)j ; B = -k
D) T = (-cos t)i - (sin t)j; N = (-cos t)i + (sin t)j ; B = k

Quizplus · Accepted Answer

The Answer of Find T, N, and B for the given space curve.
-$$\mathbf { r } ( t ) = ( 8 + t ) \mathbf { i } + ( 9 + \ln ( \sec t ) ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2 < t < \pi / 2$$
A) T = (-cos t)i - (sin t)j; N = (sin t)i - (cos t)j ; B = -k
B) T = (cos t)i + (sin t)j; N = (- sin t)i + (cos t)j ; B = k
C) T = (cos t)i - (sin t)j; N = (-sin t)i - (cos t)j ; B = -k
D) T = (-cos t)i - (sin t)j; N = (-cos t)i + (sin t)j ; B = k

Find T, N, and B for the Given Space Curve r(t)=(8+t)i+(9+ln⁡(sec⁡t))j−10k,−π/2<t<π/2\mathbf { r } ( t ) = ( 8 + t ) \mathbf { i } + ( 9 + \ln ( \sec t ) ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2 < t < \pi / 2r(t)=(8+t)i+(9+ln(sect))j−10k,−π/2<t<π/2

Find T, N, and B for the Given Space Curve $\mathbf { r } ( t ) = ( 8 + t ) \mathbf { i } + ( 9 + \ln ( \sec t ) ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2 < t < \pi / 2$