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Volume of a Parallelepiped Using Vectors

Vector spaces warmup

Find the volume of the parallelepiped formed by the vectors \(\mathbf{a} = 3\mathbf{i} + 4\mathbf{j} - \mathbf{k}\), \(\mathbf{b} = 2\mathbf{i} - \mathbf{j} - \mathbf{k}\), and \(\mathbf{c} = 3\mathbf{j} + \mathbf{k}\).
vectorsscalar-triple-productvolume-of-parallelepipeddeterminantcross-productdot-product3d-geometrymultivariable-calculuslinear-algebra

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What you need first

What this problem tests

Tests the ability to set up and evaluate a 3x3 determinant to find a geometric volume.

This is a standard application of the scalar triple product in multivariable calculus and linear algebra courses.

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