Find a vector function which describes the intersection of the two surfaces given. Use Geogebra3d to plot these surfaces and your answer to check that they match. 5. [P] Find a vector function which describes the intersection of the two surfaces given. Use Geogebra3d to plot these surfaces and your answer to check that they match. (a) The sphere r2 + y? + z2 = 25 and the plane z = 3 %3D (b) The circular cylinder r2 + z2 = 4 and the plane r+y- 3z = 6 (c) The parabolic cylinder y = r² – 2 and the elliptic paraboloid z = 1² + y? (d) The circular cylinder (z - 3)² + y² = 9 and the parabolic cylinder z = %3D (e) The planes 2r -y+3z =1 and z+5y - 2z 6

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.