3. For any vectors U, V and scalars a, b, prove that (a) (aU) x (bV) = ab(U x V)

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A: Show that dot multiplication of vectors is positive definite; that is, show that u.u>=0 for every…

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Q: (a) Using Gaussian elimination, find a vector v such that

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Q: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

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Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

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Q: (b) For any arbitrary vectors u, v and w, prove that (u x v) x w = u x (v x w) if and only if (u x…

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Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

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Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.