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

Q: 5. For the vectors = (-3, –4) and v = (-2, 2) Find the dot product u · v, and the angle 0 between…

A:

Q: Find the solution of sin² (x) – 4sin (x) – 1 = 0 for all angles between 0 and 2n.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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: 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: 2. For v = (5,-2) and w = (3, 4), find v+w, v - w, v/2, -w and make one sketch labeling all 6 of…

A: Given,           v=<5,-2> and w=<3,4>

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

A:

Q: 5. For vectors given the vectors v =(-4,-3) and w (-1,-1), find: (a) Sketch, v+w below. Find its…

A: We can solve as follows

Q: Determine the angles between the following pairs of vectors. (a) (−1, 1), (0, 1)     (b) (2, 0), (1,…

A: To determine the angles between the following pairs of vectors.

Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

A:

Q: 12 2 14- = -3 are 3 Determine if the pair of vectors V₁ = 3₂ orthogonal.

A:

Q: 1. Find A-C|(B – D) using the following vectors: A= C= D=

A:

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

A:

Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: Given vectorsu = (1,3) and v (0. -3), find u

A: Given vectors are The vector u.v is evaluated as follows

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

A:

Q: 3) |x| = 7, y = 8, and|x - y = 10, determine | x + y. Hint: sketch out these 4 vectors on the same…

A: We know that the vector parallelogram rules  ||A+B||^2+||A-B||^2=2||A||^2+2||B||^2

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: 12. Given a point P(1,-2,-4) and a point P2(3,1,-5), find a unit vector that has the opposite…

A: Step 1:Step 2: Step 3: Step 4:  thanks...