91Ó°ÊÓ

In Exercises 21-26, find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. \(\quad \quad \textit{Point} \quad \quad \quad \quad \quad \quad \textit{Perpendicular to}\) \(\quad (5, 6, 3) \quad \quad \quad \quad \quad \textbf{n}=-2\textbf{i}+\textbf{j}-2\textbf{k}\)

In Exercises 21-26, determine the octant(s) in which \((x, y, z)\) is located so that the condition(s) is (are) satisfied. \(y<0\)

In Exercises 37-40, find the lengths of the sides of the right triangle with the indicated vertices. Show that these lengths satisfy the Pythagorean Theorem. \((1, 0, 1), \quad (1, 3, 1), \quad (1, 0, 3)\)

In Exercises 47-50, find the area of the triangle with the given vertices. (The area \(A\) of the triangle having u and v as adjacent sides is given by \(A=\frac{1}{2}||\textbf{u} \times \textbf{v}||\).) \((1, -4, 3), (2, 0, 2), (-2, 2, 0)\)