Mathematics II20805 marksInner product, Length, and orthoganility
Prove that the two vectors u and v are perpendicular to each other if and only if the line through u is perpendicular bisector of the line segment from -u to v.
Prove that the two vectors u and v are perpendicular to each other if and only if the line through u is perpendicular bisector of the line segment from -u to v. [5]
The line through u means the line passing through the origin in the direction of u, i.e., the set {tu : t ∈ ℝ}. The line segment from -v to v has its midpoint at the origin (since (-v + v)/2 = 0). The line through u is the perpendicular bisector of the segment from -v to v if and only if: 1. The ...