Use normal vectors to determine the intersection, if any, for each of the following groups of...

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Advance Math

Use normal vectors to determine the intersection, if any, foreach of the following groups of three planes. Give a geometricinterpretation in each case and the number of solutions for thecorresponding linear system of equations. If the planes intersectin a line, determine a vector equation of the line. If the planesintersect in a point, determine the coordinates of the point.

a x + 2y + 3z = ?4

b x + 2y + 3z = ?4
2x + 4y + 6z = 7
2x + 4y + 6z = 7
x + 3y + 2z = ?3
3x + 6y + 9z = 5

c x + 2y + z = ?2

d x ? 2y ? 2z = 6 2x + 4y + 2z = 4 2x ? 5y + 3z = ?10 3x + 6y + 3z= ?6 3x ? 4y + z = ?1

e. x ? y + 3z = 4 x + y + 2z = 2 3x + y + 7z = 9

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Solve the system of equations x1 2x2 3x3 42x1 4x2 6x3 73x1 6x2 9x3 3 Simplify the system x1 2x2 3x3 42x1 4x2 6x3 7x1 2x2 3x3 1 From 1th equation we find x1 by other variables x1 2x2 3x3 42x1 4x2 6x3 7x1 2x2 3x3 1 In 2 3th equation substitute x1 x1 2x2 3x3 422x2 3x3 4 4x2 6x3 72x2 3x3 4 2x2 3x3 1 After simplification we get x1 2x2 3x3 40 150 3 Answer The system of equations has no solution because 0 3 BSolve the system of equations x1 2x2 3x3 42x1 4x2 6x3 73x1 6x2 9x3 5 From 1th equation we See Answer

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