Write the mathematical form of unit vector.
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To find a unit vector with the same direction as a given vector, we divide the vector by its magnitude. For example, consider a vector v = (1, 4) which has a magnitude of |v|. If we divide each component of vector v by |v| we will get the unit vector uv which is in the same direction as v.
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Let, iˆ jˆ and kˆ be three unit vectors which specify the directions along positive x–axis, positive
y–axis and positive z–axis respectively.
These three unit vectors are directed
perpendicular to each other, the angle
between any two of them is 90°. iˆ,jˆ , and k.ˆ are examples of orthogonal vectors.
Two vectors which are perpendicular to
each other are called orthogonal vectors
as is shown in the Figure
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