The plane x + y + 2z = 20 intersects the paraboloid z = x² + y² in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at ). Point nearest occurs at ).

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A: P=3, 7, 3Q=9, 1, 8To find M, the midpoint of PQ.M=?  

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. (1 - x)y' = y2

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Q: Evaluate the integral i- te*j + VTk] dt 0,

A: ∫03t2i - tet2j + t7/2k dt [t3i/3 - et2j/2 + 2t9/2k/9 ]03 9i - e9j/2 + 2*35/2k (9 , -e9/2 , 235 )

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A: We can find the required answer as below.

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A: In this question, we need to find the angle θ between the given two vectors.