3. Q=16=x² + y² +z² +4xy+4.xz – 4yz Find the principal axes by finding a suitable rotation matrix for the quadratic form given by. Detemine the geometric shape for the value of Q=16. (ellipsoid, sphere, etc.)(showing all intemediate operations)

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: The figure below shows four named points A, B, C, and D on a grid generated by two vectors 7₁, 72 in…

A: We have to write each vector as a sum of scalar multiples of v1 and v2.

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Q: Given the points M[0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector…

A: This question can be solved using the concept of finding the vector joining two points and dot…

Q: 15m Please explain how to get the i, j, k, vectors of A, B, and C.

A: To find the vectors A, B and C.

Q: Write the 3D Rotation Matrix around the y-axis by 0 = 45°:

A: Introduction: One kind of transformation matrix is the rotation matrix. This matrix serves as a tool…

Q: 2. Let A (1,-1,0) and B = (2,1,-2). (a) Solve for projgA. (b) Find the angle between projgA and A.

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Q: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4 represent in…

A: Given: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4…

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Q: Find the triple scalar product (u xv). w of the given vectors. u= -5i - 3j+ 4k v=5i - 8j + 4k…

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Q: Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use…

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Q: Violet now comments that there are scalars a and B such that di DE = a EF × EG = B GF x GD State the…

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Q: Let u= (2,-3, 2, 5) and v a- i b- = (1, 2, 0, -4). Find scalars a and b so that au + bv = (0, -7,2,…

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Q: Solve 2 part only in 30 min nd take a thumb up plz

A:

Q: Convert the quaternion (1,0,0,0) to a rotation matrix.

A: Given information:A quaternion .To Find:Convert this quaternion into a rotation matrix.Concept…

Q: Find the scalar projection ofb onto a when b = i- j-3 k, a= i+2j+ 2k. 1. scalar projection -2 5 2.…

A: The given vectors are b=i-j-3k and a=i+2j+2k

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A: The given problem is to find all solutions of Ax=0 in the parameteric vector form with the given…

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Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b =(3, 3, 1) compab = 3.571428…

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Q: De termine if the vectors 2 re lincarly independent or linearly dependent Please explain your answer

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Q: Topic: Vectors and Geometry of Space → identify and sketch the following item. identify its traces…

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A: We can answer it as below

Q: Select the correct answer. 2x Which matrix represents the rotation of the vector (, 4) by 3 radians?…

A: In the given question we have to find the matrix which represents the rotation of the vector 1, 4 by…

Q: 1. Consider A = 8i-12j, B = 2i + 14j and C= 18i-10j. (a) In R² space, draw the vectors A, B, and C…

A: