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Mathematics Question on Vector Algebra

Find the scalar components and magnitude of the vector joining the pointsP(x1,y1,z1)andQ(x2,y2,z2). P(x_{1},y_{1},z_{1})and Q(x_{2},y_{2},z_{2}).

Answer

The vector joining the points P(x1,y1,z1)and Q(x2,y2,z2)can be obtained by,
PQ→=\overrightarrow{PQ}=position vector of Q−Q-Position vector of PP
=(x2−x1)i^+(y2−y1)j^+(z2−z1)k^=(x_{2}-x_{1})\hat{i}+(y_{2}-y_{1})\hat{j}+(z_{2}-z_{1})\hat{k}
|PQ→\overrightarrow{PQ}|=(x2−x1)2+(y2−y1)2+(z2−z1)2=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}
Hence,the scalar components and the magnitude of the vector joining the given points are respectively{(x2−x1),(y2−y1),(z2−z1)(x_{2}-x_{1}),(y_{2}-y_{1}),(z_{2}-z_{1})}and (x2−x1)2+(y2−y1)2+(z2−z1)2.\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}.