Question

Determine if the two vectors u = –3i – j and v = 2i + 2j are orthogonal. If they are not orthogonal, specify the angle between them

Answer 1

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