The rectangular coordinates of a point are (1, 0) . Plot the point and find two sets of polar coordinates for the point for 0 ≤ θ < 2π.

Q: Evaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by…

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Q: Find the angle made by the vectors A and B given below A=(2,1,3). B=(3,-2,1).

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Q: If k is any positive number, what is the size of the angle between the vectors a = (k, k) and b =…

A: The angle between the vector a→ and b→ is define by the following formula. cosθ=a→·b→a→b→

Q: : Let x and y be non-parallel vectors. Prove that (x + y) and (x - y) are vectors perpendicular to…

A: For two vectors A→ and B→, the angle between them is θ. The dot product of these vectors…

Q: Given the matrix 3. 4 6 -7 Find the Characteristic Equation and find its solutions (aka:…

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Q: Consider the vectors A = (-5.4, 8.8) and B = (8.7, -9.4), such that A - B + 3.8C = 0   What is the x…

A: Let the coordinates for point C be (x, y).For the given coordinates of A and B, vector…

Q: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

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Q: Find the Miller Indices of a plane whose intercepts are (2,1,3).

A: Given intercepts are (p,q,r)= (2,1,3) The Miller indices of a plane is    h,k,l=1p,1q,1r…

Q: Evaluate the given integral. Jx²Inxdx

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Q: show that the function y(x)=Ax^n (A and n are constants) will give a straight line on a log-log…

A: The provided function is expressed as y=Axn

Q: If the Cartesian coordinates of a point are given by (-1, y) and its polar coordinates (r, 120°).…

A: given that    Cartesian coordinate =( -1 , y )  put  X = -1    Y = y polar coordinate =( r, 120°)…

Q: Find the general solution of the given differential equation that is valid in any interval not…

A: Given, x2y''-3xy'+4y=0 ___(1) To find general solution of the equation

Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }

A: To solve the given question, we will write down the given two vectors in vector form and then we…

Q: Suppose thatP = (x, y) has polar coordinates(r, θ ). Find the polarcoordinates for the points:  (−x,…

A: Given: The point P is (x,y). The polar coordinates are (r,θ). The coordinates of the point are…

Q: Given the following matrix 3 3 1 5 Find its two eigenvectors. (A 3 and H2 0. B 3 and A, !! R -3 and…

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Q: Let P:(-1,2,3), Pa(2,-1,1) and Pa(1,1,1) area of the triangle equal..

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Q: If A = 4i − 3k and B = −2i + 2j − k, find the scalar projection of A on B, the scalar projection of…

A: The given vectors are, A=4i-3kB=-2i+2j-k

Q: If f is a scalar function and v = [v1, v2, v3] is a vector field. Show that div(fv)=f divv+v·∇f

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Q: Find the divergence and rotation of the following vector A=i(x^2+y^2)+j(y^2+zx)+k(z^2+xy)

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Q: Let A=5i-6.5 and B=3.5i-7ĵ . If lies in the xy-plane, Cis perpendicular to À , and Č-B=15 , what is…

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Q: prove that A ⊕ B Equal to inverse of Y= ĀB+AB̄

A: A xor B is given by A' B + AB' Given, Y = A' B + AB' Y' = (A' B + AB') ' Y'  = (A'B) '. (AB')'  Y' =…

Q: Evaluate the integral. 5/t +² 2 dt

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Q: Show that the points with position vectors 3i-5j, 4į+j, 6¿+13j are collinear. If the point whose…

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Q: Let C be the plane curve given parametrically by the equations : x(t) = t² - t and y(t) = t² + 2t -…

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Q: Find the distance from the origin to the plane 3x − 2y − 6z = 7

A: The equation of the plane is, Now, compare the above plane with the general form of the plane (ax +…

Q: Find the measures of the angles between the diagonals of the rectangle whose vertices are A = (5,…

A: Vertices of rectangle: A(5,6), B(8,12), C(-40,36), D(-43,30)  When we'll plot these vertices on…

Q: nates of point N. 2) Write the vector KM in terms o

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Q: Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there…

A: Let’s consider the following sets of vectors,

Q: Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise…

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Q: Which of the following is the conserved quantity if the system having Lagrangian L= = m(x² + y²) – ²…

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Q: Consider a cube with one corner at origin and the other corner along the body diagonal at (1,1,1).…

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Q: P-1 Show the given set of function is orthogonal and find the Norm of the function in given set {cos…

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Q: To find the vertical asymptote of a graph of a rational function, you set the numerator equal to…

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Q: If F = (2x2 - 3:) î – 2xy j - 4xk, then evaluate , V F dV, where V is bounded by 1. x = 0, y = 0, z…

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Q: Find D in cartesian coordinates) at P(6,8,-10) caused by a uniforms surfacecharge density p,…

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Q: Consider the following scalar and vectors: Ã = 41+ 3) + 7k T = 3x+8yz + 2zx 1. Calculate for the…

A: REQUIRED  LAPLACIAN. DIVERGENCE.

Q: prove that F(x, y, z) = (3x² + .

A: Solution:

Q: Consider the curve described by the parametric equations x =t+ cos t, y = 2 – sin t. Compute the…

A: Slope or tangent to a curve in  X-Y plane is given as dY/dX.

Q: . Using the differential length dl, find the length of each of the following segments/curves: a) 2 <…

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Q: Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of…

A: The cross product property of vectors is given by:u×v=uvsinθ......(1)where,u and v are the magnitude…

Q: Given ϕ=xy+yz+xzϕ=xy+yz+xz, find gradient ϕ at point (1, 2, 3).

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