NINAY.docx - Introduction to vector analysis 1 Consider the...

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Introduction to vector analysis1.Consider the vectors PQ and RS in R3, where P = (2,1,5), Q = (3,5,7), R = (1,−3,−2) and S=(2,1,0). Does PQ= RS?
2.Determine the distance between the points P = (2,−1,4) and Q = (4,2,−3) in R2.
3.Calculate the area of the triangle ∆PQR, where P=(2,4,7),Q=(3,7,18),andR(−5,12,18).
4.Calculate the area of the parallelogram PQRS, where P =(1,1), Q =(2,3), R=(5,4),and S=(4,2).
6.Convert the point (−2,−2,1) from Cartesian coordinates to (a) cylindrical and (b) spherical coordinates.
7.Write the equation (x2)2+(y1)2+z2=9in spherical coordinates.
8.Find the intersection (if any) of the spheresx2+y2+z2=25x2+y2+(z2)2=16.

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