Given a point P(1,1,2) and a plane a in R' defined by the equation 2a + y-22 = 0. (a) Find an equation of the line, passing through the point P. that is perpendicular to the given plane a. (b) Find the minimum distance from the point P to the given plane 7. (c) Use orthogonal projection to find the point of intersection of the plane a with the line found in part (a).

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

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Q: b) Obtain the equation of a plane, P that is orthogonal to the line L:x=1+4, y=8+1, z =9+9t_and goes…

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Q: Find the distance from the point Q = (1, -3, 3) to the plane 2x + 2y + 5z = 2.

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Q: 3. The vertices of a triangle are A(1, -2), B(4, 4) and C(-3, 0). (a) Find the distance between A…

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Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

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Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

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A: Since you have uploaded multiple question, according to our guidelines we have solved first question…

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