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Question
Find the position vector of midpoint M joining the points L(7, –6, 12) and N(5, 4, –2).
Solution
The position vectors `vecl` and `vecn` of the points L(7, –6, 12) and N(5, 4, –2) are given by
`vecl = 7hati - 6hatj + 12hatk, vecn = 5hati + 4hatj - 2hatk`
If M(`vecm`) is the midpoint of LN, by midpoint formula,
`vec"m" = (vecl + vecn)/2`
= `((7hati - 6hatj + 12hatk) + (5hati + 4hatj - 2hatk))/2`
= `1/2 (12hati - 2hatj + 10hatk) = 6hati - hatj + 5hatk`
∴ Coordinates of M(6, –1, 5)
∴ Hence, position vector of M is `6hati - hatj + 5hatk` and the coordinates of M are (6, –1, 5).
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