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Sum

Find the position vector of midpoint M joining the points L(7, - 6, 12) and N(5, 4, - 2).

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#### Solution

The position vectors `bar"l"` and `bar"n"` of the points L(7, -6, 12) and N(5, 4, -2) are given by

`bar"l" = 7hat"i" - 6hat"j" + 12hat"k", bar"n" = 5hat"i" + 4hat"j" - 2hat"k"`

If M(`bar"m"`) is the midpoint of LN, by midpoint formula,

`bar"m" = (bar"l" + bar"n")/2`

`= ((7hat"i" - 6hat"j" + 12hat"k") + (5hat"i" + 4hat"j" - 2hat"k"))/2`

`= 1/2 (12hat"i" - 2hat"j" + 10hat"k") = 6hat"i" - hat"j" + 5hat"k"`

∴ coordinates of M(6, - 1, 5).

Hence, position vector of M is `6hat"i" - hat"j" + 5hat"k"` and the coordinates of M are (6, - 1, 5).

Concept: Section Formula

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