MATH125 Lecture Notes - Lecture 7: Hypotenuse, Unit Vector

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

Let u and v be nonzero vectors in rn. (0 180 ) between u and v by cos = u v. Compute the angle between the vectors u = We compute u v = 2 1 + 1 1 + ( 2) 1 = 1, ||u|| = 22 + 12 + ( 2)2 = 9 = 3 and ||v|| = 12 + 12 + 12 = 3. Using a calculator we nd that is approximately equal to 78. 9 . The concept of perpendicularity is fundamental to geometry. In r2 two nonzero vectors u and v are perpendicular if the angle between them is a right angle, i. e. = /2 radians or = 90 . It follows that u v = 0. Two vectors u and v in rn are orthogonal to each other if u v = 0. 2 are orthogonal to each other. u =