Define vector triple product and explain its significance?
Saturday, December 16, 2023
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Question: Define vector triple product and explain its significance?
The vector triple product is defined as the cross product of one vector with the cross product of the other two. In mathematical terms, it is expressed as **a × (b × c)** . This resulting vector is coplanar with vectors **b** and **c** and is perpendicular to **a** .
The vector triple product can be simplified using the following formula:
**a × (b × c) = (a . c) b - (a . b) c**
This is known as the **triple product expansion**, or **Lagrange's formula** .
The vector triple product has some applications in physics and geometry. For example, it can be used to find the torque exerted by a force on a rigid body, or to find the area of a triangle given its three vertices
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