Exercise 3 Let L be the line in R spanned by the vector u = Its orthogonal complement L is a plane in R. 1) Give an equation for the plane L. 2) Find an orthogonormal basis (52, b) for L. ()-- 3) Find the orthogonal projection of v = 2 on L.

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Let P be the like (-1,0,2) . Consider the plane that goes through the points A=(3,4,-1), B=(1,-3,3)…

A:

Q: Considering the points P (1, 2, 3), P (−2, 0, 4) and P (3, 4, 6). a) formulate a vector equation for…

A:

Q: 3. A scalar equation of the plane with normal vector = [0, -1, 3] and passing through the - point…

A: Topic = Geometry Correct option = A

Q: (v) Find the equation of the plane II that consists of all linear combinations of u, v. (vi) Is the…

A: use linear combination

Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,-1,0) •…

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Q: (a) Determine the vector equation and the Cartesian equation of the plane B passin by the points…

A: This is a problem of vector calculus.

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.