# Triple Product Calculator

The calculator will calculate the triple product (both scalar and vector) of the three vectors, with steps shown.

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Calculate $\left(-2, 3, 1\right)\cdot \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right)$, $\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\cdot \left(-3, 2, 1\right)$, $\left(-2, 3, 1\right)\times \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right)$, and $\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\times \left(-3, 2, 1\right)$.

## Solution

• Calculate the scalar triple product $\left(-2, 3, 1\right)\cdot \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right)$.

$\left(-2, 3, 1\right)\cdot \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right) = \left(-2, 3, 1\right)\cdot \left(-4, -7, 2\right)$ (for steps, see cross product calculator).

Next, $\left(-2, 3, 1\right)\cdot \left(-4, -7, 2\right) = -11$ (for steps, see dot product calculator).

The scalar triple product can be found as the determinant that has three vectors as its rows or columns.

• Calculate the scalar triple product $\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\cdot \left(-3, 2, 1\right)$.

$\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\cdot \left(-3, 2, 1\right) = \left(4, 7, -13\right)\cdot \left(-3, 2, 1\right)$ (for steps, see cross product calculator).

Next, $\left(4, 7, -13\right)\cdot \left(-3, 2, 1\right) = -11$ (for steps, see dot product calculator).

The scalar triple product can be found as the determinant that has three vectors as its rows or columns.

• Calculate the vector triple product $\left(-2, 3, 1\right)\times \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right)$.

$\left(-2, 3, 1\right)\times \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right) = \left(-2, 3, 1\right)\times \left(-4, -7, 2\right)$ (for steps, see cross product calculator).

Next, $\left(-2, 3, 1\right)\times \left(-4, -7, 2\right) = \left(13, 0, 26\right)$ (for steps, see cross product calculator).

• Calculate the vector triple product $\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\times \left(-3, 2, 1\right)$.

$\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\times \left(-3, 2, 1\right) = \left(4, 7, -13\right)\times \left(-3, 2, 1\right)$ (for steps, see cross product calculator).

Next, $\left(4, 7, -13\right)\times \left(-3, 2, 1\right) = \left(33, 35, 29\right)$ (for steps, see cross product calculator).

$\left(-2, 3, 1\right)\cdot \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right) = -11$A
$\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\cdot \left(-3, 2, 1\right) = -11$A
$\left(-2, 3, 1\right)\times \left(\left(7, -4, 0\right)\times \left(-3, 2, 1\right)\right) = \left(13, 0, 26\right)$A
$\left(\left(-2, 3, 1\right)\times \left(7, -4, 0\right)\right)\times \left(-3, 2, 1\right) = \left(33, 35, 29\right)$A