Quaternions and spatial rotation around the "z" axis, then flip it 180 degrees around the "x" axis. Take the other book, flip it 180° around "x" axis first, and 90° clockwise around "z" later. The two books do not end up parallel. This shows that, in general, the composition of two different rotations around two distinct spatial axes will not commute. The vector cross product, used to define the axis–angle representation, does confer an orientation ("handedness") to space: in a three-dimensional vector space, the three vectors in the equation will always form a right-handed set (or a left-handed set, depending on how the cross
Right angle to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry. A rectangle is a quadrilateral with four right angles. A square has four right angles, in addition to equal-length sides. The Pythagorean theorem states how to determine when a triangle is a right triangle. In Unicode, the symbol for a right angle is . It should not be confused with the similarly shaped symbol . Related symbols are , , and . In diagrams, the fact that an angle is a right angle is usually