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Show that the equation represents a sphere, and find its center and radius.4x2+ 4y2+ 24x+ 4z2−20y=−57...

Show that the equation represents a sphere, and find its center and radius.4x2+ 4y2+ 24x+ 4z2−20y=−57 + 16z.

Find a unit vector that has the same direction as the vector 3a−2b given that a= 2i+k and b=i−j+ 3k.

Find a vector b with |b|= 5 such that the angle between the vector a=〈0,2〉and the vector b is π/3.(Hint: cos(π/3) =12).

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