5. Consider a unit vector u = (a,b). (a) How many unit vectors are orthogonal to u? (b) Explain a process for finding all of them. (e) Show that for any three vectors = (a,b), y = (c,d), = (e, f), we have 7- (ÿ+2) = 7-ÿ+ ž· ž.

Q: 1. y -2+ 2.

A:

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

A:

Q: 5. (a) Given A = a,5-ay2 + a₂, find the expression of a unit vector of B such that B/A and BL A, if…

A: Solution 5(a): Given that A→=5ax-2ay+az and  B→∥A→ if B→ lies in the xy-plane. So, B→=5bx-2by. Unit…

Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

A:

Q: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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Q: why are the position vectors of D, E, F (b+c)/2, (a+c)/2 ect and not D= (c-b)/2, E= (c-a)/2, F=…

A: The objective is to determine why are the position vectors of D, E, F are b+c2,a+c2, and…

Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

A:

Q: Q2/ (a) Let A (2,3,0) and B (-1,- 2,- 4) be two points. Find the vector AB in terms of the standard…

A: The detailed solution is as follows below:

Q: A river is flowing in a straight line from the point A(1,3) to the point B(5, 1). A town is located…

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: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: 5. Let A = (4,3), B = (0, 1), and C = (−3, 7). (a) Find the vectors AB, BC, and AT. (b) Prove that…

A: Step 1:It is provided that, A=(4,3),B=(0,1), and C=(−3,7). (a) Then, it is obtained:AB=B−A…

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: mine the angle between vectors M = (1

A: Here we vector M=1,2,5 and vector T=-2,-3,3

Q: Find the vector v, where u = (-2, 3) and w = (-3, -2). Su + w) Illustrate the specified vector…

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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: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

A: