Show that if u = u₁i + u2j + uzk is a unit vector, then the arc length parameter along the line r(1) from the point Po(xo, yo, Zo) where / = 0 is / itself. = (xo + tur)i + (yo + tu₂)j + (zo + tuz)k

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: Two unit vectors that are parallel to the tangent line to the curve y= 2sinx at the point (t/6, 1)…

A: To solve the given question , we must know the slope of the tangent line to the curve y=2sinx at…

Q: Find a vector equation with parameter tt for the line of intersection of the planes x+y+z=4x+y+z=4…

A: What is Plane: A plane is a flat, two-dimensional surface that never ends in mathematics. A plane is…

Q: Determine the interval (s) on which the vector-valued function r(t)=ti+(sqrtt+1j)+(t^2+1)k…

A: The answer is given below:

Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: 3. The position vector of a particle moving in the plane is given by r(t) = e *'i+ e'j. a) Find the…

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Q: Let a > 0 be real. Use residues to evaluate the princi- pal value of the integral R 1+ cos ax lim…

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Q: Find the unit tangent vector T, the unit normal vector N, and the binormal vector B for curve r at…

A: Here we are given the curve r(t)=(7cost,7sint,7ln(cost))We have to find the unit tangent vector…

Q: Let f(x, y, 2) = cos(ryz) Find the directional derivative of f at the point (,, 7) in the (a)…

A: We have to find Directional Derivative and Largest possible value.

Q: Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt. n'=dxn, h' = d x b and…

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Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: Find T, N, and B for the curve r(t) = (14t, 14t, e') at (0, 0, 1). %3D Hint: After finding T', plug…

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Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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Q: 7. On a two-dimensional plane, sketch the vector |v>= such that it emanates from the coordinate…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n' = dxn, b' = d xb and…

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Q: consider the vector-valued function r(t) = a) State the domain of r(t) b) Identify where r(t) is…

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