The Difference Between the Lines š + tš and š + t(š − š)
The Difference Between the Lines š + tš and š + t(š − š) A line in vector form is defined by two components: a base point that determines its position, and a direction vector that determines its orientation. Two expressions may involve the same vectors but still represent completely different lines when either the base point or the direction vector changes. The expressions L₁: š + tš L₂: š + t(š − š) provide a clear example of how distinct lines arise from different vector components. 1. Line L₁: š + tš The expression š + tš describes a line passing through the point represented by vector š with direction vector š. As the real parameter t varies, the expression generates all points on the line. Base point: š Direction vector: š This is the line through š directed along š. 2. Line L₂: š + t(š − š) The expression š + t(š − š) describes a different line. Its base point is š, and its direction vector is t...