For each of the following bilinear forms b : V × V → R, state whether b is product and explain why. b(u, v) = U1V1 + 3U1V2 – U2V1 + UQV2, where V = R² and u = (u1, U2), V = (V1, v2) are two vectors in V.

Q: Consider three vectors u = 3i +j+ ak, = 2i + bj +k, = -4i + (b – 2)3 + (b+ 8)k, where a and b are…

A: The solution are next step

Q: Consider the following vectors. u (6, –5) and v = (9, 1) u + v = (12, – 3) | (c) Find 7v – u. 7v – u…

A: By algebra of vectors we solve the this question.

Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: Determine the value of k for which the vectors u and v are orhogonal u = (1, k, –3), v = (2k, –5, 6+…

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Q: 1. Add the following three vectors to find the resultant vector, R: šj = (-2,0)m, .ž= (0,–5,)m, .řz…

A: 1.   x1¯  =  (-2,0)mx2¯  =  ( 0, -5)mx3¯   =  (3,0)m Now , In the East - west direction ,  we deal…

Q: Let ū= 2 + 2Ĵ - 2k and J = 2î - 2Ĵ + k. + Verify that the vectors i and I are perpendicular and have…

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Q: For the following three vectors, what is 2. Ć ·(3 Á × B )? В = 3.00î + 3.00ĵ – 4.00k B = - 3.00î +…

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Q: For the vectors u=−1,4 and v=−4,2​, calculate projvu and scalvu.

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Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: given u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  determine a,b so that v are parallel vectors

A: Given that, u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  We have to determine a,b so that u and v are…

Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: If --0--0---0 1 and v3 = 0 then the vectors V1, V2, and v3 are linearly dependent. Select one: O…

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Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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Q: The cross product (u x v) of the two vectors u = i-2j + k and v = 3i + j - 2k is -3i - 5j7k. True

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Q: Let us consider two vectors in R³: u = (2, -3,5) v = (a, b, c) Find the values of a, b, and c such…

A: Two vectors are orthogonal if their dot product is zero.The dot product of two vectors u→=⟨u1,u2,u3⟩…

Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

Q: Find a vector, w, which is perpendicular to the vectors where u=61-15 Ĵ + 7k and v= -19 1+53 - 5 k.…

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

A: Vector: An object which has both magnitude as well as direction is called a vector. We can draw a…

Q: For the vectors u = (1, 2, 0) and v = (2, 1, 3) , evaluate the following expressions. a. 2u + 4v c.…

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Q: Consider the vectors ā (2, 3, –1) and b = (4, –9, 6). Find the cross product of a and b

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Q: Consider two vectors u = bi+k and v= 3bi+bj - 2k. Determine b to have u and 7 orthogonal.

A: Here two vectors are given and it is given that they are orthogonal so we have to find the value of…