Find B and t for the space curve r(t) = (5 sin t) i + (5 cos t) j+(12t) k. 12 T = i+ sin 13 CoS j+ k 13 13 N = (- sin t) i+(-cos t) j The binormal vector is B= Oi+ (Oj+ k. The torsion is t = (Type an integer or a simplified fraction.)

Q: Find the vector and parametric equations for the line through the point P(4, -2, -4) and parallel to…

A: Find the vector and parametric equations for the linethrough the point P4,-2,4 and parallel to the…

Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

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Q: Find a vector G with curlG = sin xk.

A: Let F → = d1i+d2j+d3kThen curve F → =∇xF → =ijkddxddyddzf1f2f3Let us consider G→ = g1i+g2j+g3kThen…

Q: Find the parametric equations for, the tangent line to the curve It)=4?+1) i t (t+ 4)Ĵ ť 3+3 R at…

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Q: Find the angle between the surfaces x² + y² + z² = 49 and z = x² + y² - 7 at the point (3,-2, 6):

A: Since you posted multiple questions, as per Bartleby guidelines we are answering here first…

Q: Find the tangent plane to the equation z = 3y cos(5x – 2y) at the point (2,5,15) z =

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: Describe the curve represented by the vector-valued function r (t) = (2 cos t) i +tj + (2sin t) k…

A: Given: r→(t) =2costi→+tj→+2sintk→. x=2costy=tz=2sint Then, x2=costz2=sint

Q: The transformation Po[1, ₂] = cos²0 cos sin cos sin sin²0 [1, ₂] onto the line through the origin…

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Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin (t)) at t = 3…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Let r(t) = (15, cos t, -3 sint) be the position vector of an object. Find the velocity and speed of…

A: Given that rt=15,cost,-3sint  find the velocity and speed of the object