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Question
Find the scalar components and hence magnitude of the vector joining the points P(x1,y1,z1) and Q(x2,y2,z2).
Find the scalar components and hence magnitude of the vector joining the points P(x1,y1,z1) and Q(x2,y2,z2).
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Solution
The vector joining the points P(x1,y1,z1) and Q(x2,y2,z2) can be obtained by,
PQ=PV of Q−PV of P=(x2^i+y2^j+z2^k)−(x1^i+y1^j+z1^k)=(x2−x1)^i+(y2−y1)^j+(z2−z1)^k
∴ Scalar components of PQ are x2−x1, y2−y1, z2−z1.
∴ Magnitude of |PQ|=√(x2−x1)2+(y2−y1)2+(z2−z1)2
The vector joining the points P(x1,y1,z1) and Q(x2,y2,z2) can be obtained by,
PQ=PV of Q−PV of P=(x2^i+y2^j+z2^k)−(x1^i+y1^j+z1^k)=(x2−x1)^i+(y2−y1)^j+(z2−z1)^k
∴ Scalar components of PQ are x2−x1, y2−y1, z2−z1.
∴ Magnitude of |PQ|=√(x2−x1)2+(y2−y1)2+(z2−z1)2
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