Scalar product

In this video I show you how the scalar product or dot product can be used to find the angle between two vectors.

    • \text{If }\mathbf{a}=a_1\mathbf{i}+a_2\mathbf{j}+a_3\mathbf{k}\text{ and }\mathbf{b}=b_1\mathbf{i}+b_2\mathbf{j}+b_3\mathbf{k}

\text{then}

\cos \theta = \dfrac{\mathbf{a}.\mathbf{b}}{|\mathbf{a}||\mathbf{b}|} \text{ where }\mathbf{a}.\mathbf{b}=a_1b_1+a_2b_2+a_3b_3

IMPORTANT: Take note of the directions of the vectors.

Finding the interior angle of a triangle

In this video I show you how the scalar product or dot product can be used to find the interior angle of a triangle.

Example

  1. If A(2, -1, 4), B(-3, 2, 1) and C(5, 3, 2). Find the size of angle ABC.

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