Distance Formula
Category : JEE Main & Advanced
(1) Distance formula: The distance between two points \[A({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}})\] and \[B({{x}_{2}},\,{{y}_{2}},\,{{z}_{2}})\] is given by
\[AB=\sqrt{[{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}+{{({{z}_{2}}-{{z}_{1}})}^{2}}]}\].
(2) Distance from origin : Let \[O\] be the origin and \[P(x,y,z)\] be any point, then \[OP=\sqrt{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}\].
(3) Distance of a point from co-ordinate axes : Let \[P(x,y,z)\] be any point in the space. Let \[PA,PB\] and \[PC\] be the perpendiculars drawn from P to the axes \[OX,\,\,\,OY\] and \[OZ\] respectively.
Then, \[PA=\sqrt{({{y}^{2}}+{{z}^{2}})}\]
\[PB=\sqrt{({{z}^{2}}+{{x}^{2}})}\]
\[PC=\sqrt{({{x}^{2}}+{{y}^{2}})}\]
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