Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <7, -4>, v = <-28, 16>

Answer 1

The vectors u = < 7, -4 > v = < -28, 16 >

Calculate the angle between the vectors by using following formula

cos θ =(u.v)/|u||v|

u . v = < 7, -4 > . < -28, 16 >

u . v = 7(-28) + (-4)(16)

u . v = - 196 - 64

u . v = - 260

Calculate the magnitude of vectors.

Magnitude of a vector |a| = √(x² + y²)

|u| = √(49 + 16) = √65

|v| = √(784 + 256) = √1040

cos θ = u.v/|u||v|

= -260/(√65)(√1040)

cos θ = -260/√67600

cos θ = -260/260

cos θ = -1

θ =  180 degrees

Angle between two vectors is 180 degrees.

Therefore, the vectors u and v are  parallel with opposite direction.