Question

Define unit vector and explain it in detail.

Answer 1

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A unit vector is any vector that has a magnitude of one and could be pointing in any direction.

Such vectors are usually used to specify directions and therefore they do not have any dimension or unit like other vectors (e.g. m/s for velocity or m/s (sq) for acceleration)

The unit vectors in the positive direction of x, y and z axis are labelled as i,j and k respectively with a small hat on top. They are used to express other vectors by combining the magnitudes of those vectors with i,j and k. Example a vector V having magnitude “a” in x direction and magnitude “b” in y direction can be written as

V = ai + bj (V needs to have an arrow on top while i and j should have cap as per the proper notation)

IT is simply a vector of unit length with the same direction as a given vector. If a given vector already has unit length, then it is its own unit vector; otherwise, one way of expressing any vector is as its length ("magnitude"), which is a scalar, times a unit vector having the same direction as the given vector: in essence, the unit vector is the direction of the given vector (and therein lies its primary use: as the basis for expressing any vector having the same direction but arbitrary length).

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