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

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 359 People

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

Answered by maham237 @ 25/12/2020

Vectors are orthogonal if their dot product is equal to zero:
u · v = 7· 21 + 2 · 6 = 147 + 12 = 159 ≠ 0
Vectors are parallel if the angle between them is 0°, or cos ( u, v ) = 1
cos ( u, v ) = ( u · v ) / ( | u | · | v | ) =
= 159 / (√(7² + 2²) · √(21² + 6²) ) =
= 159 / ( √ (49 + 4 ) · √ ( 441 + 36 ) ) =
= 159 / (√53 · √477 ) = 159 / 159 = 1
Answer : The vectors u and v are parallel.

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