Question: that passes through the origin. 3. (a) Draw a picture that shows the direction angles a, , and y of a vector. (b) What

that passes through the origin. 3. (a) Draw a picture that shows

that passes through the origin. 3. (a) Draw a picture that shows the direction angles a, , and y of a vector. (b) What are the components of a unit vector in 2-space that makes an angle of 120 with the vector i (two answers)? (c) How can you use vectors to determine whether a trian- gle with known vertices P1, P2, and P3 has an obtuse angle? (d) True or false: The cross product of orthogonal unit vec- tors is a unit vector. Explain your reasoning. 4. (a) Make a table that shows all possible cross products of the vectors i, j, and k. (b) Give a geometric interpretation of ||u v||. (c) Give a geometric interpretation of u (vxw)|. (d) Write an equation of the plane that passes through the origin and is perpendicular to the line x = t, y = 2t, z = -t. 5. In each part, find an equation of the sphere with center (-3, 5, -4) and satisfying the given condition. (a) Tangent to the xy-plane (b) Tangent to the xz-plane (c) Tangent to the yz-plane

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