50. Find the vector from the origin to the point of intersection of the medians of the triangle whose vertices are А(1, -1, 2), В(2, 1, 3), and C(-1, 2, -1).

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

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Q: 1. y -2+ 2.

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

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Q: Which of the following pairs of vectors are perpendicular to each other? a) (4, 14, -18) and (6, 21,…

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Q: Find the vector in R³ from point A = (–4, 7, 6) to B = (–8, –5, 7). AB: =

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Q: Q1: suppose the middle of each side of the triangle is a vector from the vertex (1,2,3), (3,2,1),…

A: Vectors

Q: Consider the vectors A= (4, -2, 2), B =-(-2,3,0), and C= (0, 2, 1). 1. Find the following. (a) B- A…

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Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: 15. Which is the component form of the vector shown? -2- * (1, 2) -4 (-5, -3) O (4,-7) O (7.-4)

A: This question is related to vectors, we will solve it using given information

Q: Find the area of the triangle with vertices (1, 1, 2), (2, 3, 5), and (1, 5, 5). Use vectors and…

A: Consider the given question, Let the vertices of the triangle ABC is A(1, 1, 2), B(2, 3, 5) and C(1,…

Q: Show that the vectors (1,0,1); (-1,2,3) and (0, 1; -1) spans R³

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Q: Line E goes through the points (1, 5, 2) and has the direction vector ⟨2, 2, 3⟩. Line F goes through…

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Q: Suppose that v1 = (5, 2, 0, 3), v2 = (2, -2, 8, 2) and v3 = (-6, 0, 5, 4). Is the following vector…

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Q: Suppose that v1 = (5, 1, 0, 5), v2 = (5, -3, 6, 2) and v3 = (-5,0, 5, 2). %3! Is the following…

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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: 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: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: Find the vector equation for the line of intersection of the planes 4x - y + 3z = 1 and 4x + 2z = −1…

A: Given:equation of two planes To find:vector equation of line that intersects these planes

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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Q: 3) Which two vectors are perpendicular? a = [-10, -2, -4] 6= [3,-3, 6] = [5, 1, -2]

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Q: Write a = 18 (0, 3, 0) as the sum of two vectors, one parallel and one perpendicular to b = If a = a…

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Q: lowing vector in the span{V₁, V₂, V3}? 8,9) me vector is in the span. me vector is not in the span.

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Q: Suppose that v1 = (4, 1, 0, 4), v2 = (2, -4, 5, 2) and v3 = (-2, 0, 3, 6). Is the following vector…

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Q: 5. Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2)…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.