Determine if u = -2 I + j and v = I + 2 j are orthogonal, parallel, or neither. Show all your work that supports your answer
To determine if two vectors are orthogonal, we need to calculate their dot product and check if the result is equal to zero. If the dot product is zero, the vectors are orthogonal. If the dot product is not zero, we need to check if the vectors are parallel by comparing their directions.
Given vectors u and v:
u = -2i + j
v = i + 2j
Calculate the dot product of u and v:
u . v = (-2)(1) + (1)(2)
u . v = -2 + 2
u . v = 0
Since the dot product of u and v is zero, the vectors are orthogonal.
Therefore, u and v are orthogonal.