Let d be metric on X, and de f ined di on X as di = max (d (r, ).0}, then dis semi metric but not metric C not well defined O

Q: A stream line is a line that is everywhere tangent to the velocity filed 0 صواب ihi O

A: False

Q: Plane R is tangent to sphere 0 at point T. How are radius OT and plane R related?

A:

Q: The directional derivative of o = xy²z+ 4x'z at (-1,1,2) in the direction 2i +j- 2k. ans. 38 - 38 3.…

A:

Q: 3. Let C be the circle x + y = 16 and let S be any surface above the xy-plane with C as its…

A:

Q: E valuate f win Tydy tyxdx olE Cethe line seqment f&Om (0,2) to

A: on solving this we get the

Q: 1. Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), -5 ≤ t ≤ 5 b) r(t) = √ēti +…

A:

Q: 4. Does there exist a simple closed unit-speed plane curve with curvature less than or equal to 2…

A: In a simple closed unit-speed plane curve, curvature =1r According to the question, Area of the…

Q: Consider the directional derivative of the general function z =, = f(x,y). a) Where is it a i)…

A: The directional derivative of function φ=z-f(x,y) at (a,b,c) in the direction of u…

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: 9. GIVEN: QU || DA, QU DA. PROVE: AUXQ ADXA.

A:

Q: The curvature of a function y = f(x) is given by the expression y" (1 + (y')²)³/2 Determine a…

A:

Q: Find the curvature of ƒ(x) = ln cos x, < x < 2 -- 2°

A:

Q: 2. Calculate the curvature, unit binormal vector and torsion for r(t) (e'cost)i+(e'sint)j +5k

A:

Q: The curvature of a point moving along the curve given as R(t)=(In sec t) i+ tj is: O t O sec t O…

A: Here, Rt=lnsecti+tj

Q: The curvature of r = 1+ cos 0, 0: 2 2/2 5 2/2 3/3 2 3/3 3.

A: Given: r=1+cosθ,θ=π2 κθ=2f'θ2+fθ2-fθf"θf'θ2+fθ232   r=f(θ)r=1+cosθ f'θ=-sinθf"θ=-cosθ

Q: Pind the curvature x of the curve given by 7(()- (V2)i+ (e)j+(e)k, at the point P(0, 1, 1),

A: Curvature K = |r' x r"|/|r'|^3

Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

A:

Q: Show that the shortest distance between the principal normal at con 1/2 secutive points distance s…

A:

Q: Determine the curvature of the graph of y = In x at the point where x = 1.

A:

Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: 8. Given the space curve C as the image of the vector valued function r(t) = 2ti+t³j+-t-¹ k OR r(t)…

A:

Q: 8. [*] for position vector (t-1, 3-2t, 4t-t') find [*] the unit tangent [**] the unit normal, the…

A:

Q: If F(x, y, z) = z - f(x, y) and s is the graph of z = f(x, y) and (a, b,c) is a point on the surface…

A:

Q: solve for the following using the concepts of vector calculus:

A:

Q: Find the displacement of an object on the interval 2 ≤ t ≤ 5 if its velocity is shown. V(Đ m 3 1 5 7…

A: Given: A graph of velocity-time.

Q: d (x, y) = (x - y)^2 does the function define a metric o

A: