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

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Solution

Let the midpoint of $P Q$ be $R$
Position vector of $P = (2 - 0)^i + (3 - 0)^j + (4 - 0)^k$
$\to O P = 2^i + 3^j + 4^k$
Position vector of $Q = (4 - 0)^i + (1 - 0)^j + (- 2 - 0)^k$
$\to O Q = 4^i +^j - 2^k$
Now,
Position vector of $R = \frac{\to O Q + \to O P}{2}$
$\to O R = \frac{(4^i +^j - 2^k) + (2^i + 3^j + 4^k)}{2}$
$\to O R = \frac{(4 + 2)^i + (1 + 3)^j + (- 2 + 4)^k}{2}$
$\to O R = \frac{6^i + 4^j + 2^k}{2}$
$\to O R = \frac{2 (3^i + 2^j +^k)}{2}$
$\to O R = 3^i + 2^j +^k$
Therefore, position vector of midpoint of $P Q$ is $3^i + 2^j +^k$

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Similar questions

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

P (2, 3, 4)

Q (4, 1, - 2)

R

P

Q

2 \to a + 3 \to b

\to a - 3 \to b

1 : 2

P

R

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

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