scalar triple product

Question

The scalar triple product [a⃗ b⃗ c⃗] represents

RankGuru · Accepted Answer

1. **Definition**: The scalar triple product is $[\vec{a}, \vec{b}, \vec{c}] = \vec{a} \cdot (\vec{b} 	imes \vec{c})$.
2. **Geometric Significance**: The cross product $(\vec{b} 	imes \vec{c})$ gives the area of the base and a normal vector. The dot product with $\vec{a}$ scales this by the height of the figure.
3. **Conclusion**: It equals the **volume of the parallelepiped** formed by the three vectors as edges.

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scalar triple product

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More scalar triple product Practice Questions

Three vectors $\vec{a}$ , $\vec{b}$ , $\vec{c}$ are coplanar if their scalar triple product is

scalar triple product

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More scalar triple product Practice Questions

Three vectors a⃗\vec{a}a, b⃗\vec{b}b, c⃗\vec{c}c are coplanar if their scalar triple product is

Three vectors $\vec{a}$ , $\vec{b}$ , $\vec{c}$ are coplanar if their scalar triple product is