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

Sum

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

#### 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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