5. The function r(t) = (2 sin (¹), 3, 2 cos (7)) parametrizes (draws) the path of a particle moving in 3D space. (a) Evaluate r(t) at t = 0, 1, 2, 3, 4.

Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

A:

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

Q: 2. If r(t) = ti + cos(t)j + sin(t)k, evaluate (a) frit r(t) dt, (b) r' (t) (c) the parametric…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: (a) z(t) = (2 +3i)(1 – t) + (4 + 7i)t, 0 st<1, (b) obtained by writing the equation of the line…

A: This is a problem of Complex line Integral.

Q: x(t) y(t) = 3 sin t 8 cos t 0<t< 2n a) What does the curve described by these parametric equations…

A: Recall: Equation of line: y-y1=mx-x1 ; where m=dydx or  y2-y1x2-x1 Length of the curve…

Q: Problem. Consider the helix R(t) = cos(2t)î + sin(2t)ĵ + 4tk (a) Compute R'(t) and R"(t) (b) Compute…

A:

Q: A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos…

A:

Q: baseball is hit at 120 ft/sec from the ground at a 300 angle to the horizontal from a height of 3…

A:

Q: Given a velocity field: V = 1.8 ( rz (1-sin²(0))) er + 2.8 (1-cos2(0)+ rz) eg +1.8 ( rz tan(0)…

A:

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: 3. Triangle DEF with vertices D(0, 6). E(3.5), and F(1, 1): 90° counterclockwise about the point…

A: Rotation is a rule of transformation. Through this transformation, one can produce a new image by…

Q: -1

A: Given,

Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…