Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the intersection of this plane with the line parallel to the vector A = ⟨1,1,1⟩ and passing through the point S = (−1,0,0).

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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

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Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

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Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

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Q: Find a unit vector with positive first coordinate that is orthogonal to the plane through the points…

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Q: Find the vector equation of the plane that contains the parallel lines [x, y, z]= [0,1,3] + [-6,…

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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: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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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: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

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Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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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.