Two vectors by definition are orthogonal when the angle between them is 90 degrees.
It can also be said that they are orthogonal if the scalar product between both vectors is zero.
We have then:
u = -3i - j
v = 2i + 2j
u.v = (- 3i - j) (2i + 2j) = - 6-2
u.v = -8
They are not orthogonal vectors.
The angle between them is
lul = root ((- 3) ^ 2 + (-1) ^ 2) = 3.16227766
lvl = root ((2) ^ 2 + (2) ^ 2) = 2.828427125
The angle between them is:
cos (x) = (u.v) / ((lul) * (lvl))
cos (x) = (- 8) / ((3.16227766) * (2.828427125))
cos (x) = - 0.894427191
x = acos (-0.894427191)
x = 153.4349488
x = 153.43
Answer:
It is not orthogonal
Angle between them:
x = 153.43
