a) Show that if u, v, and w are differentiable vector functions of t, then d du V X w +u - dt dv dw (u ·v × w) dt X w + u•v x - dt dt b) Show that

Q: Let u be a unit vector. Show that the directional derivative Duf is equal to the component of V f…

A: Here, u be a unit vector. The directional derivative of Duf is equal to the component of ∇f along u…

Q: Let fery) Ts TS a diff eran tiable function. eron The directional Jeri ve dive of fuiyl in the direc…

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Q: Match the following vector-valued function with its graph. r(u,v) = u cosvi+u sinvý + uk 3. C. e 3…

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Q: Use the function to find the image of v and the preimage of w. T(V,, V2) = (v, + V2, V - v2), v =…

A: Linear transformation: Let us consider a mapping T:V→W defined as T(v)=w where v∈V and w∈W [  v is…

Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: True or False: Given a function of two variables f(x, y), the vector Vf(a, b) is perpendicular to…

A: It is false. The gradient vector ∇fa,b is not perpendicular to the graph z=fx, y at the point with…

Q: 2.31 Let A and B be vector functions of position vector x with continuous first and second…

A: Let A and B be vector functions of position vector x with continuous first and second derivatives,…

Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

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Q: Prove that the tangent vector is always orthogonal tothe position vector for the vector-valued…

A: Given r(t) =⟨sin t, sint cos t, cos2 t⟩.  we need to prove that the tangent vector is always…

Q: f(x, y, z) = sin(ry + z) foksiyonunun| P(1, 7/4, 7/2) noktasinda v = -2i + j+ 2k

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Q: tA= ate V x V x A forr 0. T Here a is a constant vect

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Q: Find a vector-valued function whose graph is the plane x+y+z== a. r(u,v)=ui-vj-(3-u-v)k b. r(u,v)=…

A: The equation of plane x+y+z=3

Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

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Q: Show that V×(ƒ v)=ƒ(Vxv)+(Vƒ)×v for scalar function f(x, y, z) and vector function v(x,y,z)=v,…

A: Given: The scalar function is given by:                  fx,y,z The scalar function is given by:…

Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: Let / be the line through the point with coordinates (1,1,1) in the direction of the vector on [? O…

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Q: 3. Find a parametrization for (a vector valued function that traces) the line which passes through P…

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Q: Consider the function f(z,y, 2) ,>0, y>0 and the point P(1, 1, 2). a): Find the direction in which f…

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Q: Use the function to find the image of v and the preimage of w. T(Vg, V2) = (V, + V2 V1 – V2), v =…

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Q: - Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in…

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Q: The directional derivative of the function f(x, y, z) = x³y4 – 3z2 at the point (1, 1,1) in the…

A: we have to find the directional derivative

Q: The directional derivative Df is a vector parallel to u. OTrue False Reset Selection

A: We have to find that the given statement " The directional derivative Duf is a vector parallel to…

Q: Find a vector-valued function whose graph is the plane x+y+z= 12, O r(u, v)=-ui-vj+(12-u-v)k O r(u,…

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Q: Q5: Plot the function y= 2 tan(t)-cos(mt) labeling the x and y axes. Where t is a vector containing…

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Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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Q: Given the vector-valued function

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Q: Let f be differentiable function then then the quantity Vf · û where û is a unit vector is maximized…

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Q: No. 6 (a, b, c)

A: Problem concerns the geometry of the curve defined by the vector valued function

Q: ATA, B curi(A x B) = A (div B) – B (div A) + (B-V) A - (A.V) B, are two differentiable vector point…

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Q: f V f(0,0) = (3,4) then there is exactly one unit vector u for which D,f(0, 0) = 1. O True False

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