Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same x-intercept as [x, y, z]=[-1,8,6]+[-2,4,3].

Q: photo attached

A: Given point can be written in vector form as,

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A: Topic:- 3D

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Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

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A: follow next step

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

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Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

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Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

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Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

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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.