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