To prove: The equation 11.7 given in the textbook.

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Chapter 11, Problem 4P

To determine

To prove: The equation 11.7 given in the textbook.

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Use the definition of the vector product and the defini- tions of the unit vectors î, j, and k to prove Equations 11.7. You may assume the x axis points to the right, the y axis up, and the z axis horizontally toward you (not away from you). This choice is said to make the coordinate system a right-handed system. î x i = j x j = k x k = 0 i xj = -j x î = k jx k = -k x j = i k x i= - i x k = }

The cross product AxB is perpendicular to both vectors in the cross product (think of Aand В as lying on a sheet of paper; the cross product is perpendicular to the plane of the sheet). After figuring out the two directions perpendicular to both vectors you use one of the right hand rules given on Page 338 to choose which of the two direction is correct. All three should give the same result so use whichever one you are most comfortable with. In class, we will use the middle one in the diagram in the book. The vector torque is where "is the vector from the axis of rotation to where the force is applied. Which is the direction of the torque vector? +y ++ * (in) +z (out) O = in (O) = out

Find for the Cross Product of the following pairs of vectors 1. A=4i-5j +8k, B = -2i+3j+3k 2. C = -6i+4j+7k, D=4i-j+5k 3. E= -i-5j + 2k, F = 8i+2j-6k