Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, -2>, v = <8, 24>

Answer 1

The vectors u = < 6, -2> v = < 8, 24>

Calculate the angle between the vectors by using following formula

cos θ =(u.v)/|u||v|

u . v = < 6, -2> . < 8, 24 >

u . v = 6(8) + (-2)(24)

u . v = 48 - 48

= 0

Calculate the magnitude of vectors.

|u| = √(36 + 4) = √40

|v| = √(64 + 576) = √640

cos θ =u.v/|u||v|

= 0/(√40)(√640)

cos θ = 0

θ = cos^-1 (0)

θ = 90

Angle between two vectors is 90 degrees.

Therefore, the vectors u and v are  orthogonal.