(0, 0, 0)*, X2 = (1, 0, 0)", x3 = (1, 1, 0)", x4 = (1, 0, 1)*. Consider the four vectors x1 = %3D %3D Find the projected points, if the dimensions are reduced from three to two using Principal Component analysis.

Q: Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4,…

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

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A: Given plane: Let the normal vector be n. So,

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Q: 2/159 The commercial airliner of Prob. 2/90 is redrawn here with three-dimensional information…

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Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

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Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

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Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

A:

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

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Q: the component of vector a are ax=2.0 units and ay=3.0units while that of another vector b are Bx=…

A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A:

Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: 4

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Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

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Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A:

Q: Consider the four vectors X1 = (0, 0, 0)', X2 = (1, 0, 0)", x3 = (1, 1, 0)", x4 = (1, 0, 1)'. %3D…

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

A:

Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

A:

Q: What is the value of each of the constants that are part of the linear combination between the…

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Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: In what direction should one move from the point (2, 3) to increase 4x?y most rapidly? Present your…

A: The solution is given below

Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

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Q: 6.) Find a vector equivalent to the vector PQ with its initial point at the origin. = (;-2), Q =…

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

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Q: If U and V are 2 x 1 orthonormal vectors and A = UVT then the trace of A is equal to а. О b. 2 с. -1…

A: We have to find Trace of the Matrix.

Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

A: We need to find two distinct vectors on the line belonging to the intersection of the hyperplanes

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

A:

Q: Calculate the first two vectors generated by the Gauss-Seidel method.

A: Gauss Seidle method

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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Q: Two out-of-phase alternating voltages are represented by: = 3.4sin (wt +) and V, = 1.3cos (wt +).…

A: we will find horizontal and vertical component of each voltage and then represent them in vector…