The vector product of two vectors A and B is a vector and so has both a magnitude and direction: 1. Magnitude: The magnitude of the vector product Ax Bis: ||A × B|| = |A|| ||B|| sin e = AB₁ = A₁B where is the angle between the vectors. Here B₁ = B sin 6 is the component of B perpendicular to A while A₁ = A sine is the component of A perpendicular to B. Special Cases: Give answers to questions below in terms of the magnitudes A and B. What is Ax B if A and Bare parallel? If A and Bare perpendicular? 2. Direction: The direction of the vector product Ax B is perpendicular to the plane determined by the vectors A and B, and follows a "right hand rule". This "right hand rule" is different from the one we used to determine angular velocity. The steps to determining the direction of the vector product are a. Determine the two possible directions: First determine the only two possible directions that are perpendicular to both A and B. The vector product must be in one of these two directions. What are the two possible directions for Ax B for the vectors shown above? ar b. Apply right hand rule: We now use the right-hand rule to determine which of the choices is correct. • Point the fingers of your right hand in the direction the first vector (in this case A) points. • 100 With your fingers still pointing in that direction, twist your hands so that your palm faces the general direction the 2 vector points (in this case B). B What is the direction of the vector product B x A for the two vectors shown above? Note the direction of the vector product depends on which vector comes first with (Ã×B): • Stick out your thumb. This is the direction of the cross product. Make sure it is one of the two possible directions. If it is not you did something wrong. • Optional: Curl your fingers to determine the direction the torque will cause the object to spin. c. What is the direction of the vector product Ax B for the two vectors shown above? d. Let A be into the page and B point as shown. Follow the steps above and draw an arrow indicating the direction of (A x B) or write out, in or zero if the cross product is into or out of the page or zero. A (into page) B Ā Direction=