Let 0 = (0,0, 0), i = (1,0,0), j= (0, 1,0), k= (0,0, 1) be vectors in R°. Given in the figure below a cube with an edge length of 5 in. E (a) Describe all points (z, y, 2) in the cube. (b) Write down the vectors OẺ, OĎ, OF, OĞ as linear combinations of i, j,k. (c) Find the coordinates of the center point of the cube.

Q: show that the vectors: 2,3), II

A: To prove that the vectors:     v1=(1, 2, 3), v2=(-2, 1, 1), and v3=8, 6, 10 in ℝ3  are linear…

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Find the value of a so that the vectors a = (34, -22, 49), b= (5, 51, 35). and c = (a, -394, -14)…

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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: Sketch 2v, -w, v+w, and 2v-w for the vectors in Figure 24. 5 y 4 3 v = (2,3) 2 1 w = (4, 1)

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Q: Let T: R2 R be a reflection in the x-axis. Find the image of each vector. (a) (7, 6) (b) (9,-3) (c)…

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Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

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: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

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 the value of a so that the vectors a = (11, −29, 13), b = (46, 5, 37), and c = (a, -194,-70)…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

Q: (a) 3u7 u3 (b) (c) u2 (-2u5) (d) 2u2 : (-u5)

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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: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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