(6) Show that the vector equations r = -2i + j+ t(-į+ 5j) and r = -3i + 6j + s(-3i + 15j) | | refer to the equation of the same line and find the relation between s and t to give the position vector of the same point.

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: Find the vector equation of the line that goes through the point (10,15,9)(10,15,9) and is…

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Q: The parametric vector v=(6-t)i+(9t+8)j represents a straight line. Find the equation of this line

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: M] - [8] x+y -3x+y.

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: Find the point functions t= d6i +(e-6); +(-€)4 and 40=(2+2-/it (5- €);t (1-56)4 Intersect. at which…

A: Given: Two vector functions as r1t=2ti+t2-6j+-13t3k and r2t=2+2ti+5-tj+1-5tk, To find: The…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: rite the equation of the line passing through P with direction vector d in vector form and…

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Q: Find the scalar equation for each line: (a) a line through the point (-6, 7) with direction vector…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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.