Find the weighted Euclidean distance between the given vectors. = n with weights w = d(u, v) = Ex: 1

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: For y'= Aj where A is given below %3D A= find the right hand side vector F(t, ) needed to apply…

A: Given y'→=Ay→ Here A=1245 We have to find right hand side vector F→(t,y)→.

Q: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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Q: Given the vector function r(t) = (+1, 1-2t², 8t-4), find the are length of this curve on the…

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Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

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Q: find the distance d(u, v) between u and v in the given exercise.

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Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), V(PR), and V(PS) are…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

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Q: Find the normal vector N(t) to r(t) =〈4,sin 2t, cos 2t〉.

A: Given: rt=4, sin(2t), cos(2t)

Q: find the given vector  Vector of length 2 in the direction opposite to v = i − j

A: A vector oppositely directed to v=i-j is is u=-v=-i-j=-i+j                   u=-i+j A unit vector eu…

Q: Find the next vector spacing and wrap A = 1(x + y?) +jv² + zx) + k(z? + xy)

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Q: Given the vector function 7(t) = (t +3, 7t – 5) %3D Calculates the principal normal vector (t)when t…

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Q: In Fr let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: 2) If A =,find grad(div A), where r is a position vector.

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Q: Find the resaltant vector of the following using graph cal and analntical I=15km 40° East of sonth…

A: Given that T = 15km 40 degree East of South u = 25km 20 degree North-East P = 30km 15 degree West of…

Q: 3. The work Wdone by = xf + 3xyj - (x + z)k to move a particle from point 1 to point 2 is defined by…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the vectors T and N and the binormal vector B = T × N for the vector-valued function r(t) = 4…

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Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

Q: Find the cross product of the unit vectors. jx i

A: Topic :- Vector

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a…

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Q: Compute the length of the given vector. (t) = 2t + 7 and q(t) = 7t - 5, where to = 0, t₁ = 1, t₂ = 2

A: We have to find the length of the given vectors.

Q: Q. For the Spheri cal polas Coozdinates (r0,d), prove that their unit vectors mutually orthogonal?…

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Q: Find the next vector spacing and wrap A = 1(x +y) +j + zx) + k(2 +xy)

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Q: Find the vectors T and N and the binormal vector B=TXN, for the vector valued function r(t) at the…

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Q: Given the vector function. Calculates the principal normal vector N(t) when t=6.9

A: Question- Given the vector function. Calculates the principal normal vector N(t) when t=6.9 ?

Q: The unit normal vector N to the curve 7(1) = (1, t, at t=0 is

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Q: ). Determine the set Tp(Zf) of all tangent vectors to Zf at p. Is dim Tp(S) m ker d f.?

A: Sol

Q: Find the weighted Euclidean norm of the given vector. 10 with weights w = v = ||v|| = Ex: 1

A: Here, we need to find the weighted Euclidean norm of the vector v=102 with the weights w=111. Let…

Q: find the distance d(u, v) between u and v in the given exercise.

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Q: What are the possible angles 0 between two unit vectors e and f if ||e x f|| V? (Let 0 <o Sn. Enter…

A: The modulus for the cross product for 2-unit vectors e and f are given. The modulus for the unit…

Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

Q: Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P =…

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

Q: Find a unit vector perpendicular to i-j and to i +k and with a positive k component.

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Q: (b) Find a vector i that is parallel to ↑ and perpendicular to L.

A: As per your demand, we solve part b) only

Q: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

A: To find the normal unit vector perpendicular to A and B

Q: Given the unit tangent 1. (-2 sin t, 1,2 cos t). V5 and unit normal vector: n=D(-cost,0, - sin t).…

A: Given unit tangent  u=15-2sint, 1, 2cost and unit normal vector n=(-cost, 0, -sint) To find the unit…

Q: In Rn with inner product{x, y} = xTyderive a formula for the distance between two vectorsx = (x1, .…

A: Take two vectors x and y in an inner product space x=x1,…,xn and y=y1,…,yn then x,y=xTy

Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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Q: Find the unit tangent, normal and binormal vectors T, N and B for the curve at the point (0, 7, -1).

A: The curve is defined by the vector function rt=sint2,t2,cost2 on the domain [0,∞) To find the unit…

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: Find a unit vector that is orthogonal to both i +j and i + k.

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Q: d) Our goal is to find a vector ÂY such that Ax minimizes the distance from b. How does Aâx relate…

A: Let the given system be Ax=b. Assume that the system has no solution. Then we have to find the…