Mathematics II20785 marksInner product, Length, and orthoganility
Prove that the two vectors uuu and vvv are perpendicular to each other if and only if the line through uuu is perpendicular bisector of the line segment from −u-u−u to vvv.
Prove that the two vectors uuu and vvv are perpendicular to each other if and only if the line through uuu is perpendicular bisector of the line segment from −u-u−u to vvv. [5]
The line segment runs from -u to v. Its midpoint is: $$M = \frac{-\mathbf{u} + \mathbf{v}}{2}$$ The line through u (passing through the origin in the direction of u) is the perpendicular bisector of the segment from -u to v if and only if two conditions hold simultaneously: 1. u is equidistant fr...