23. Vectors and 3D question bank (Maths)

If the position vectors of the vertices of a triangle be \( 6\mathbf{i} + 4\mathbf{j} + 5\mathbf{k} \), \( 4\mathbf{i} + 5\mathbf{j} + 6\mathbf{k} \), and \( 5\mathbf{i} + 6\mathbf{j} + 4\mathbf{k} \), then the triangle is  

The perimeter of the triangle whose vertices have the position vectors \( \mathbf{i} + \mathbf{j} + \mathbf{k} \), \( 5\mathbf{i} + 3\mathbf{j} - 3\mathbf{k} \), and \( 2\mathbf{i} + 5\mathbf{j} + 9\mathbf{k} \), is given by