The two vectors j + i and 3i + j + 4k represent the sides vector (AB) and vector (AC) respectively of triangle ABC.

Question

The two vectors \(\hat j+\hat i\) and \(3\hat i+\hat j+4\hat k\) represent the sides \(\vec{AB}\) and \(\vec{AC}\) respectively of triangle  ABC. Find the  length of the median through A.

Answer 1

Let D be the point at which median drawn from A touches side BC.

Let \(\vec a,\vec b\) and \(\vec c\) be the position vectors of the vertices A, B and C.

So position vector of D = \(\cfrac{\vec b+\vec c}2\)

So we creating a vector in the direction of AD

\(\vec {AD}\) = Position vector of D - position vector of A