Vector notation
Unit vector notation

A vector in R 3 {\displaystyle \mathbb {R} ^{3}} (or fewer dimensions, such as R 2 {\displaystyle \mathbb {R} ^{2}} where v below is zero) can be specified as the sum of the scalar multiples of the components of the vector with the members of the standard basis in R 3 {\displaystyle \mathbb {R} ^{3}}. The basis is represented with the unit vectors ı ^ = (1, 0, 0) {\displaystyle {\boldsymbol {\hat {\imath }}}=(1,0,0)}, ȷ ^ = (0, 1, 0) {\displaystyle {\boldsymbol {\hat {\jmath }}}=(0,1,0)}, and k ^ = (0, 0, 1) {\displaystyle {\boldsymbol {\hat {k}}}=(0,0,1)}.

A three-dimensional vector v {\displaystyle {\boldsymbol {v}}} can be specified in the following form, using unit vector notation: v = v x ı ^ + v y ȷ ^ + v z k ^ {\displaystyle \mathbf {v} =v_{x}{\boldsymbol {\hat {\imath }}}+v_{y}{\boldsymbol {\hat {\jmath }}}+v_{z}{\boldsymbol {\hat {k}}}}

where v, v, and v are the scalar components of v. Scalar components may be positive or negative; the absolute value of a scalar component is its magnitude.
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