Find the position vector of the mid-point of the vector joining points P(2,3,4) and Q(4,1,-2).

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Solution

The position vector of mid-point of the vector joining the points P(2,3,4) and Q(4,1,-2) is given by
PV of the mid-point of (PQ)= $\frac{1}{2} (P V o f P + P V o f Q)$
$= \frac{1}{2} [(2^i + 3^j + 4^k) + (4^i +^j - 2^k)] = \frac{1}{2} (6^i + 4^j + 2^k) = 3^i + 2^j + 1^k$

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P (2, 3, 4)

Q (4, 1, - 2)

P (2, 3, 4)

Q (4, 1, - 2)

The position vector of mid-point of joining the points (2, – 1, 3) and (4, 3, –5) is:

P (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) and Q (4 \hat{i} + \hat{j} - 2 \hat{k}) .

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