Definition:Vector Triple Product
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Definition
Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be vectors in a Cartesian $3$-space:
| \(\ds \mathbf a\) | \(=\) | \(\ds a_i \mathbf i + a_j \mathbf j + a_k \mathbf k\) | ||||||||||||
| \(\ds \mathbf b\) | \(=\) | \(\ds b_i \mathbf i + b_j \mathbf j + b_k \mathbf k\) | ||||||||||||
| \(\ds \mathbf c\) | \(=\) | \(\ds c_i \mathbf i + c_j \mathbf j + c_k \mathbf k\) |
where $\tuple {\mathbf i, \mathbf j, \mathbf k}$ is the standard ordered basis of $\mathbf V$.
The vector triple product is defined as:
- $\mathbf a \times \paren {\mathbf b \times \mathbf c}$
where $\times$ denotes the vector cross product.
Also known as
The vector triple product is also known as the triple vector product.
Also see
- Results about vector triple product can be found here.
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $7$. Products of Three Vectors
- 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 5$