Therefore, w 1, w 1, w 2, w 2, and w 3 w 3 must satisfy We want to find a vector w = 〈 w 1, w 2, w 3 〉 w = 〈 w 1, w 2, w 3 〉 orthogonal to both u u and v v-that is, we want to find w w such that u Consider how we might find such a vector. In this section, we introduce a product of two vectors that generates a third vector orthogonal to the first two. The dot product is a multiplication of two vectors that results in a scalar. Calculating torque is an important application of cross products, and we examine torque in more detail later in the section. In this section, we develop an operation called the cross product, which allows us to find a vector orthogonal to two given vectors. Note that the torque vector is orthogonal to both the force vector and the radius vector. Then, we can represent torque by a vector oriented along the axis of rotation. We can use vectors to represent the force applied by the mechanic, and the distance (radius) from the bolt to the end of the wrench. This creates rotation, or torque, which tightens the bolt. The mechanic applies a force at the end of the wrench. Imagine a mechanic turning a wrench to tighten a bolt. 2.4.5 Calculate the torque of a given force and position vector.2.4.4 Determine areas and volumes by using the cross product.
2.4.2 Use determinants to calculate a cross product.2.4.1 Calculate the cross product of two given vectors.
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