Question

If the position vectors of the vertices a b and c of a ∆abc are respectively then find the vector equation of the median through the vertex a

Answer 1

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Answer 2

The vector equation of the median through the vertex a is $\vec {r}=(1-t)\vec{t}+t(\frac{\vec{b}+\vec {c}}{2} ) [t\epsilon R]$

Step-by-step explanation:

Given:

vector(O)A = vector a

vector(O)B = vector b

vector(O)C = vector c

Let D be the mid point of Bd

The vector OD = $vector\frac{(b + c)}{2}$

∴ The vector equation of the median through the vertex A is,

$\vec {r}=(1-t)\vec{t}+t(\frac{\vec{b}+\vec {c}}{2} ) [t\epsilon R]$