5. Drop a vector from the set A {sin'x,-1,1, sin 5x} to make it independent in F(-00, 00)

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (8y – 4xy) Give your answer in unit vector…

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Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: of Q tind diretion derivative of 2メ×+sin ++ll tnthedirection of vector 3.

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Q: - 5. Consider th gonal to vector (-

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Q: Compute the indicated derivative. U(t) = 5.3t2 + 5.3; U′(4) U′(4) =

A: Given: U(t)=5.3t2+5.3 Finding the derivative of the given equation : ddtU(t)=5.3ddt(t2)+ddt(5.3)…

Q: Find linearly independent vectors which generate al lutions of Ax = 0.

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Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: 2. 1 show thet vectors cre linecrly dependent or lineerly in dependont

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Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: 5- The value of the chiral vector of SWNTS if the n=8, m=6 and the first vector length equal to +1…

A: n=8 m=6

Q: The divergence of the vector G = 2i+ sin y j+ 3k is :- -8y + x3 -8y siny + cosy O Option 3 O Option…

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Q: (c) Compute the derivative of u = Vt² +2vt³.

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Q: 8- 1 į ult1)}

A: We have to use integral formula.

Q: 3. Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

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Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the…

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Q: Calculate the derivative 5¢6 23 dt dz using Part 2 of the Fundamental Theorem of Calculus. 5,6 23 dt…

A: step 1: recalling fundamental theorem of calculus Step 2: interpreting with the given question step…

Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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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: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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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: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: wing vector fields is not con

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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

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Q: 7,2 Find the critical noint(s) of al r) and use the Second Derivative Test to classify the

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Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: Apply Gauss's theorem to evaluate. A

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Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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Q: Find the flux of ỹ across S.

A: In this question we need to find the flux across the surface is part of sphere of radius 9.

Q: Compute Jo Ji1+v¥ 1 dx

A: We need to evaluate integral.

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (4y² – 5xy) Give your answer in unit vector…

A:

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

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Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

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

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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…

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Q: -) Are these pairs of vectors orthonormal or only orthogonal or only linearly independer [:]; » [] 1…

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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: Find a vector x whose image under T,

A: A=12541022011-4-9-21 ,b=12543-51The augmented matrix of the system is 12541022011-4-9-2112543-51now…

Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

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…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: