scalar triple product

Question

Three vectors a⃗, b⃗, c⃗ are coplanar if their scalar triple product is

RankGuru · Accepted Answer

1. **Definition of Coplanar**: All three vectors lie in the same flat plane.
2. **Volume Interpretation**: If vectors are in the same plane, the 'parallelepiped' they form has zero height.
3. **Condition**: Therefore, the volume (Scalar Triple Product) must be **0**.
4. **Linear Dependence**: This also implies that the vectors are linearly dependent.

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scalar triple product

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More scalar triple product Practice Questions

The scalar triple product [ $\vec{a}$ $\vec{b}$ $\vec{c}$ ] represents

scalar triple product

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More scalar triple product Practice Questions

The scalar triple product [a⃗\vec{a}a b⃗\vec{b}b c⃗\vec{c}c] represents

The scalar triple product [ $\vec{a}$ $\vec{b}$ $\vec{c}$ ] represents