If the vertices A, B, C of a triangle ABC are the points with position vectors a1 i+a2 j + a3 k, b1i + b2 j + b3k, c2j +c3k

Question

If the vertices A, B, C of a triangle ABC are the points with position vectors \(a_1\hat i+a_2\hat j+a_3\hat k,\) \(b_1\hat i+b_2\hat j+b_3\hat k,\) \(c_1\hat i+c_2\hat j+c_3\hat k\) respectively, what are the vectors determined by its sides? Find the length of these vectors.

Answer 1

Let the position vector of the vertex ‘A’ is \(a_1\hat i+a_2\hat j+a_3\hat k,\)

And similarly B = \(b_1\hat i+b_2\hat j+b_3\hat k,\) and \(c_1\hat i+c_2\hat j+c_3\hat k\)

Side AB is

Equation (1) vector representation of the side AB

Magnitude of side AB,