show that }I f,lm) Ck-m) 2.

Q: (a) Express the mass M of a thin wire in 3-space as a line integral. (b) Express the length of a…

A: a) The objective is to express the mass M of a thin wire in 3-space as a line integral. The mass of…

Q: The vectors x and y are each of length 3 units (ie. |x| = |y| = 3)). If |x+y| = square root 17, then…

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Q: define: unit vector

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Q: Find area of triangle whose vectors Р (3,3, 1), Р2-1,0,2), Р3(2,3,3)

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Q: How many Potenhally defferent tensors of ander two can be defined by faking the ouer Product of sö…

A: The outer product of two tensors results a tensor with the order that equals the sum of the co…

Q: Define Vector Line Integral.

A: A line integral is the integral of some function along a curve. One can integrate a scalar-valued…

Q: If vector u =(7,6) and v= (-3,5) then  Find u•v

A: Given ,  If vector  u = (7,6)  v = (-3,5)  We have to find dot product u•v

Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

Q: bounded by the parall tus rectum. bounded by the parall axis.

A: Given as, The parabola y2=8x  latus rectum (x=2)

Q: Find the distance between u and v.u = (0, 1, −1, 2), v = (1, 1, 2, 2)

A: Given:U=(0,1,−1,2)V=(1,1,2,2)To determine the distance betweenU and V.

Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

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Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

A:

Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: Calculate the area of the parallelogram which is bounded by two vectors given as www ā = (x, y,z),…

A: Calculate area

Q: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7) r(t)…

A: Given: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7)…

Q: State why (u, v) is not an inner product for u = (ui, u:) and v = (v, V2) in R? %3D (u, v) = (u,v;)²…

A: We are given that u,v=u1v12+u2v22 for u=u1,u2 and v=v1,v2 in R2. We know that an inner product must…

Q: 1 Let u1 = 3 U2 = -1 , Uz = ,X = then write x as sum of two vectors -3 3 on in span {u1} and other…

A: Given, u1=1101 u2=-13-1-2 u3 = 101-1 x=1-1-33

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

A:

Q: Find a non zero unit vecor û that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: Cross product of two vector is perpendicular to both vectors.

Q: If the components of a contravariant tensor in x' coordinate system are (8,4). Show tha its…

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Q: Calculate the cross product assuming that u × v =〈1, 1, 0〉, u × w = 〈0, 3, 1〉, v × w = 〈2, −1, 1〉 v…

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Q: – 4V5 )ds]

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Q: The angle between (0, –6, 2) and (4, 8, 7) is: O A. orthogonal - O B. acute.

A: We will use geometric definition to determine the angle.

Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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Q: The scalar product of two vectors is defined as the product of their magnitudes times the of the…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R3 if x = [1,-2,4] and…

A: Cauchy schwarz inequality -  For any vectors u and v in an inner product space V,  |&lt;u,v&gt;|…

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: O True False

A:

Q: Let = . Let S be the triangle with corners at (3, 1, 2), (3, 4, 2), and (0, 4, 2), oriented away…

A: Given that v→ = 1, 2, 3 and S is a triangle with corners at 3, 1, 2, 3, 4, 2 and 0, 4, 2 oriented…

Q: Scalar mutiple of z=(4,3,-2)

A:

Q: Kinetic energy is vector ylgn İhi

A: Kinetic energy has magnitude but do not has any direction

Q: Let f:[a,b] is Riemann integr only if it is Riemann integr

A: We have to solve given problem:

Q: Determine the area of the right half of the cardioid formed by r = 7 +6 sine 14 12 10 8 6 4 -2 -4…

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Q: Find the distance between u and v. u = (-2, -1, 1, 2), v = (-1, –1, 2, 2) d(u, v)

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Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A: The line integral ∫CF·dr involves the integration over a specific path. In this problem, the…

Q: segment from ( 0,3,0) to (1, 3,7).Use line integral and check answer by caleulating (s.y.)

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Q: Sketch planeglven by Iz-31 = 1Z + lomplen the Cunve in the |ス-3| - |N+3i| 2. 2. 2. =フナ

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Q: Write down the condition of tidal resonance in terms of a (mean ocean width), lambda, and n; where n…

A: The tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect…

Q: Find the volume of the region defined by the vectors. 7 -2

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Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

A:

Q: Prove the Sum and Di¡erence Rules for vector functions.

A: Let the vectors are, We have to prove,

Q: to Dara bala y=XZ. Find the unit vectors that are parallel to the tangent line Dara bola y = x² at…

A:

Q: Evaluate the directional derivative Duf (2, 3) if ƒ (x, y) = and u is the unit vector in the same…

A: Given problem:- Evaluate the directional derivative Duf(2, 3) if f(x, y) = x/(x2 - y) and u is the…

Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: True False

A: We know that The length of a vector with two elements is the square root of the sum of each element…