The geometric definition of the period product says that the dot product in between two vectors \$vca\$ and \$vcb\$ is\$\$vca cdot vcb = |vca| |vcb| cos heta,\$\$where \$ heta\$ is the angle in between vectors \$vca\$ and \$vcb\$.Although this formula is nice for understanding the nature of the dot product,a formula because that the dot product in regards to vector components would do it much easier to calculate the period product in between two given vectors.

You are watching: Evaluate the dot product of the vectors in (figure 1).

As a an initial step, us look at the period product between standard unit vectors, i.e., the vectors \$vci\$, \$vcj\$, and also \$vck\$ of size one and parallel to the name: coordinates axes.

The standard unit vectors in 3 dimensions. The traditional unit vectors in 3 dimensions, \$vci\$ (green), \$vcj\$ (blue), and \$vck\$ (red) are length one vectors that suggest parallel to the \$x\$-axis, \$y\$-axis, and also \$z\$-axis respectively. Relocating them through the mouse doesn"t readjust the vectors, together they always suggest toward the positive direction the their respective axis.

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