Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <7, 2>, v = <21, 6>

Answer 1

The vectors u = < 7, 2 > v = < 21, 6 >

Calculate the angle between the vectors by using following formula

cos θ =(u.v)/|u||v|

u . v = < 7, 2 > . < 21, 6 >

u . v = 7(21) + (2)(6)

u . v = 147 + 12

u . v = 159

Calculate the magnitude of vectors.

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

|u| = √(49 + 4) = √53

|v| = √(441 + 36) = √477

cos θ = u.v/|u||v|

= 159/(√53)(√477)

cos θ = 159/√25281

cos θ = 159/159

cos θ = 1

θ =  0 degrees

Angle between two vectors is 0 degrees.

Therefore, the vectors u and v are  parallel.