When three vectors are added graphically and form a closed triangle, the largest enclosed angle between any two of the vectors cannot be greater than O 90°. O 180°. O No maximum exists.

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: The unit vector from A(4, 2) to the point B(-2, 10) is:

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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 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: Let's try! Using both parallelogram and polygon methods, find the resultant of the following…

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Q: Th unit vector from the origin {i.e. the point (0,0)} to the point B (3,4) is:

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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: Show that for orthogonal coordinate systems gij= 0 for i not equal to j

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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: Show that if a matrix is orthogonal and its determinant is +1, then each element of the matrix is…

A: Let A is an orthogonal matrix with determinant equal to+1. Orthogonal matrix, AAT=1…

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: Evaluate the surface integral /| (2xzdydz + ydzdx + z?dxdy) where S is a closed surface, given by S:…

A: Given:I = ∯S 2 xz dy dz + y x dx dz+…

Q: (Vector analysis) Given the function v with cubic volume having sides of length 2 from the origin as…

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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: 45° 45°

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Q: "If both x and y components of a vector A are positive, then the range of angle will be"

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Q: 4. (20%, ABET-e). Determine the coordinates of the centroid of the area by direct integration.…

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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: Suppose the vectors i,j,pand q are all unit vectors and the angle 0 = 225'. Find the cartesian…

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Q: der a cube whose edges are each of unit length, One corner coincides with the origin of an xyz…

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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: Two vectors Á and B have precisely equal mag- nitudes. For the magnitude of A + B to be 100 times…

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Q: @ Avector A of of 30 with avectorB of enath 6units. Lengith 10 units makes an angle Find the…

A: Given two vector A and B . A= 10 units and B= 6 units. The angle between two vector is 30° We have…

Q: *Problem 3.17 The 2 x 2 matrix representing a rotation of the xy-plane is cos 0 - sin 0 cos e T =…

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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: Suppose that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?

A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ

Q: If A = (x²y)î + (2y z)j+ (xyz?)k, find the gradient of the divergence of A at the point (-1,1,-2)…

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Q: Find the simplest SI unit of z, if Z = Fr³r? m³v²

A: Write the given values of this problem.  Let, F=force (kg.m/s2)r=radius mt=time secm=mass…

Q: A particle P is projected from a point O on a horizontal plane with speed 63.7 m/s at an angle 0 to…

A: Speed of the projectile,  Acceleration due to gravity,  Launch angle,    The time of flight for the…

Q: directed

A: The forces can be represented as,

Q: If v×w =2i −3j+2k, v×w=2i−3j+2k, and v⋅w=5, and θ is the angle between v and w, then

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Q: 1-36. Find the value of the integral fs A da, where A = xi - yj + zk and Sis the closed surface…

A: Find the value of the integral fs A day, where A = xi - yj + zk and Sis the closed surface defined…

Q: prove that F(x, y, z) = (3x² + .

A: Solution:

Q: If you project a tennis ball at speed v0 on a horizontal surface, what must the angle of the…

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Q: Q.1CC)IFE igen value of matrix is d, the corresponding eigen for matrix -882 vector is Lil 32 then d…

A: Given: The matrix is given as Let X be the Eigenvector matrix.

Q: If a regular polygon has 18 sides, find the measure of each interior angleand the measure of each…

A: Each interior angle of a n sided polygon will be given by following formula: Take n = 18…

Q: given a circle of radius a, find by integration using polar coordinates (d) its circumference…

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Q: and b, have magnitudes 4m and 5m, respectively. Vectorc= (a+ b). Considering all possible…

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

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