11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: 6. Write DÉ as a linear combination of the vectors i and j a) D (9,-6) E (-7, 2) first write in…

A:

Q: 39. Given a = (3, -4) and b = (1, 2). Find the vector 2 a. (3,4) a. b. 2,4) c. (6,-8) d. (5,-2)

A: From the given statement,

Q: Let P(-1, 1, 3) and Q(-3, 1, 5) be points in R3. Find the components, magnitude and direction angles…

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: 11. Given vector u = (2, a, 3), vector v = (1, -3, b) and u x v = (13, -5, -7). Find a and b.

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Q: 10. Find a unit vector in the same direction as PQ if P = (5, 4) and Q (3, 7). %3D

A: The solution is given as

Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

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Q: 40. Given a = (3, –4) and 5 = (1, 2). Find the vector a + 25. O a. (5,-8) Оь. ( 5,0) O c. (4,-4) O…

A:

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: 27. Determine the area of the parallelogram formed by the vectors u=[3,-2,5] and v=[-1,4,2].

A: Step 1:

Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

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Q: Consider the vectors i = (6,4), i = (-2,6), = (4, 2), and i = (-2, 3). Which of these vectors are…

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Q: Consider the vestun . il 1:= V2: V3: and u where a E R. (a) For which values of a is the span(v1,…

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Q: Determine if the three vectors lie in the same plane: a = (-2, 1, 3) and b = (3,-2,4), and =(-19,…

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Q: Find two different combinations of the three vectors u = (1,3) and v = (2,7) and w = (1,5) that…

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Q: Q3/A/ If ā = i – 2j + k , Find: i) (ā x b). (ā x c) ii) (ā × 5) × (ā x c) tho vectors 2i - i+ 2k and…

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Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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Q: b) For what values of h, vector u = (h, -3, -5) can be written as a linear combination of the…

A: Vector u= (h,-3,-5)Vector v1 = (1,0,-2)Vector v2 = (-2,1,7) Vector u can be written as linear…

Q: For the given vectors u and v, find the cross product u x v. *- (₁₁-1-1) u x V = u = (-2, 6, 3), v =

A: