Consider the points P = (3,2, –1), Q = (-1,1,1), and R= (-3,0,2). %3D (a) Find parametric and cartesian equations for the plane P1 that goes through the three points. (b) Find cartesian equations for the plane P2 that goes through the point P and is perpendicular to both Pi and to the plane with equation x – 4y + 2z = 4. (Hint: the perpendicularity condition means that a normal vector to P2 needs to be orthogonal to both a normal vector of Pi and to a normal vector of the plane with equation x – 4y + 2z = 4. And you do know how to find a vector that is orthogonal to two other vectors.) 2.

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Q: plane

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Q: a)What is the distance between the point A(3,1,-1) and the plane 4x + 4y +7z +2=0 ? b) Find the…

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Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

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Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

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Q: Answer the question in the picture.

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A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.