(5) Consider the plane defined by x+y+z+5= 0. Let (ro, Yo, zo) be an arbitrary point in R³ and let (2*, y, z) be the point in the plane that is closest to (zo. yo. 2o). (a) Using optimization, show that the distance D between (ro, yo, 2o) and (x, y, z) is given by co + yo +20 + 51 D(10:30, 20) (b) Using the above, compute the minimum distance between the plane and the curve defined by x² + y² = 2; 2 = 0.

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A: our objective is to find the equation of plane.

Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

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Q: Find an equation of the plane that is parallel to the line of intersection of the planes x-y+ 2z = 3…

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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 distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

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Q: Find ((x2 + 4y)i + 3 y j) · dř where C consists of the three line segments from (1,0,0) to (1,4, 0)…

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: B) The line passes through the point (2,4,5) and perpendicular to the plane 2x+y- intersects the x-y…

A: Given that the line passes through the point (2, 4, 5) and perpendicular to the plane 2x+y-5z =21