1) Find the distance and the midpoint between the points (1, -2, 3) and (4, 4, 1).
Dist:
Midpt:
2) Find the equation of a sphere with center (3, -4, -1) and radius 6.
3) Given the vectors \(\vec{v} = 3\vec{i} - 2\vec{j} + 5\vec{k}\) and \(\vec{w} = -\vec{i} + 4\vec{j} + 2\vec{k}\), find the following:
a) \(2\vec{v} - \vec{w} =\)
b) \(\vec{v} \cdot \vec{w} =\)
c) \(||\vec{v}|| =\)
d) \(||\vec{w}|| =\)