Use the inner product < f, g >= = f(x)g(x)da in the vector space Cº[0, 1] to find < ƒ,g >, ||f||, |19||, and the angle Of between f(x) and g(x) for f(x) = -5x² - 6 and g(x) = −9x + 5. (f,g) = ||f|| = ||g|| 0fg radians.

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

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Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: Let F and G be vector-valued functions such that F(t) = (cos(nt), e²t-1, t² – 1), Ġ(1) = (1, 1, –…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: If vector A = [4/1] and vector B = [-3/2] find A-B

A: Here two vectors A and B are given we have to find A-B.

Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: Find the length of the vector x=x= |x|=|x|=

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Q: Use the function to find the image of v and the preimage of w. T(Vy. V2) = ( V2, 2v1 - v2), v = (7,…

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Represent the line segment from P to Q by a vector-valued function. P(4, 0, 7), Q(3, -3, 4) r(t) =…

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Q: Determine where the vector function r(t) = i + (14t) j is continuous. Use symbolic notation and…

A: Please see the below picture for detailed solution.

Q: For this problem, enter your vectors with angle-bracket notation: , not in ijk- notation. (a) F =…

A: The solution are next step

Q: Consider the following function and point F f(x, y) = /E (a) Find the unit vectors in the direction…

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Q: Find a vector orthogonal to the line x+y=1

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Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

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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: Given the vector: j(x) sin(2x) X = X ,ex, 1-√1+x (2, 1,-2), x = 0 Determine its domain and show it…

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Q: Given V = {(x, y) |x>0} where (21, 31) (x2, Y2) = (x₁x2, Y₁ + y₂) and co (x, y) = (xe, cy), which…

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Q: sketch the space curve represented by the vector- valued function and give the orientation of the…

A: The given curve are (i) r(t)=-t+1i+4t+2j+2t+3k. (ii) r(t)=t,t2,23t3. To Sketch: The given curves…

Q: 18 > (a) Find the direction for which the directional derivative of the function f (x, y) = 7xy² +…

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Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…