Question

If
abc   
,, are the position vectors of the vertices A, B and C respectively of ABC then find the vector equation of median through the vertex A

Answer 1

Given, a, b, c are position vectors of the Vertices A, B, C.

Median of the triangle is The line joining the median point of the opposite side to the Vertex.

By section formula,

If a point P divides a line joining a, b in the ratio m:n then,

P = mb + na / m + n

Given,

OA = a

OB = b

OC = c

Mid point of BC in vector form is given by, b + c /2.

Let this point be D.

So, OD = b + c /2

The median through the Vertex A passes through A, D.

The vector equation of a line passing through p, q is given by,

at + (1 - t )b, where t is a scalar.

So, The vector equation of median through A is, (1 - t) a + t/2 ( b + c ), where t is a scalar.