Given plane z: 3x+2y+z-3=0, point P(1, -2, 3), and lines 1₁:an 4₂: (3, 6,-5)+(2, 3, 1), find: d) the Cartesian equation of the plane parallel to both line , and I, passing through point P:

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Q: Find the distance from the point (7, -14, -21) to the plane:  2x - 3y - 6z = 1

A:

Q: Find the equation of a plane bisecting the line segment joining (2,0,6) and (6,2,4) and…

A:

Q: Let A:(-1, 1, –1), B:(2,0, 2), C:(4, 1, –3), and D:(-3, 1, 10) be points in R. (a) Find the angles…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: Find the intersection of the line and plane: 3z (2x + y) = -5, P = ( r(t) = (3,-1,0) + t (-3, -2,…

A: Given line : r(t)= (3,-1,0)+t(-3,-2,-1) Given plane : 3z-(2x+y)=-5                       2x+y-3z-5=0…

Q: 3) Find equations for the lines: h the no e. The line through (1,1,1) parallel to the z-axis. f. The…

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Q: Find an equation for the plane through A(-2, 0, -3) and B(1, -2, 1) that lies parallel to the line…

A: Given points are