Prove that if u is orthogonal to v and w, then u is orthogonal to cv + dw for any scalars c and d. getting started: to prove that u is orthogonal to cv + dw, you need to show that the dot product of u and cv + dw is 0. (1) rewrite the dot product of u and cv + dw as a linear combination of (u v) and (u w) using properties 2 and 3 of theorem 5.3. (2) use the fact that u is orthogonal to v and w, and the result of part (i), to lead to the conclusion that u is orthogonal to cv + dw.

Given: △abc, ab=15, bd=9 ad ⊥ bc , m∠c=30°. find: the perimeter of the triangle.

Two lines parallel to a third line are parallel to each other. always sometimes or never

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.