Linear combination Let u = (1, 2, 1), v = (1,−1,−1), w = (1, 1,-1), and z = (2,−3,−4). Find scalars a, b, and c such that z = au + bv + cw.

Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

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Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

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Q: Calculate the scalar triple product u (vx w), where u = . (Use symbolic notation and fractions where…

A: Here we have to evaluate the scalar triple product u. (v x w) .

Q: Compute (u v Ղա • Ա. . — u = (i, 7,6), v = (2, -7i, 1+i), w = (7-i, 7i, 3 + 6i) u · v) ա • Ա —

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Q: 3. Solve the system below using the specified method. Write your answer in vector form. X1 - 3x2 = 2…

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Q: Find u × v and show that it is orthogonal to both u and v. u = v =

A: Given u→=-1,0,7v→=8,-4,0

Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 3) Verify that it is orthogonal to both a…

A: Given vectors are  a={4,5,0} and b={1,0,3} We have to find a×b

Q: Are the vectors u = [3_2_0],7 = [-3_5 −4] and @ = [1 0 -2] linearly independent? linearly…

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Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: Find w such that 2u + v – 3w = 0. u = (2, 7, 5, 0), v = (-3, 1, W =

A: Addition and subtraction of two vectors: Add or subtract the necessary components to add or subtract…

Q: Calculate the dot product of ?=(−4,−2,7,−3)and ?=(−3,1,5,8)

A: Given vector is u→=−4,−2,7,−3 and v→=−3,1,5,8. We have to calculate the u→⋅v→.…

Q: Let u = (−3,2,1,0), v = (4,7,−3,2), and w = (5, −2, 8, 1). Find the components of −u+(v−4w)

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Q: Let ā = (−1, 1, 3) and 6 = (0, -4, k). a Find k so that a and b will be orthogonal. k =

A: k=34​Explanation:   Two vectors are orthogonal if their dot product is zero.   Therefore, k=34​   (…