91Ó°ÊÓ

Find a vector \(\mathbf{v}=(a, b)\) that is represented by the directed line segment \(R \vec{S}\). Then sketch both \(\overrightarrow{R S}\) and the position vector of the point \(P(a, b)\). \(R(5,10), \quad S(-5,-10)\)

A point moves on a sphere centered at the origin. Show that its velocity vector is always tangent to the sphere.

Find (to the nearest degree) the three angles of the triangle with the given vertices. \(A(1,0,0), \quad B(1,2,0), \quad C(1,2,3)\)

Given the fact that Jupiter's period of (almost) circular revolution around the Sun is \(11.86\) yr. calculate the distance of Jupiter from the Sun.