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Components of a vector

Figure 12

Consider a vector with length a, Figure 12. Let the angle it makes with the x-axis be θ. The angle is always measured by starting with the positive x-direction and rotating anti-clockwise until the vector is reached.

The x component of the vector, denoted ax, is given by


The y component is given by


These relations hold for any angle θ, even if it is more than 900.

Convince yourself that these relations hold for the four cases where the vector with its tail at the origin, has its head in each of the four quadrants.

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