Modulo 12 2 9 2 Dirección tan 9 12 tan 075 1 075 Sentido NorEste b

Modulo 12 2 9 2 dirección tan 9 12 tan 075 1 075

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Modulo: |?| = 12 2 + 9 2 |?| = √144 + 81 |?| = √225 |𝑨| = ?? Dirección: tan 𝜃 = 9 12 tan 𝜃 = 0.75 𝜃 = ?𝑎? −1 0.75 𝜽 = ??. ??° Sentido: NorEste b. Dados los siguientes vectores en forma polar |?| = 2 ; 𝜃 = 120° ? ? = 2 ∗ ??? 120° ? ? = 2 ∗ ??? 120° ? ? = 2 ∗ ??? 225° ? ? = 2 ∗ −0.5 ? ? = 2 ∗ −0.7071 ? ? = −1 ? ? = 1.732 ? ̅ = (−?, ?. ???)

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|?| = 3 ; 𝜃 = 60° ? ? = 3 ∗ ??? 60° ? ? = 3 ∗ ??? 60° ? ? = 3 ∗ 0.5 ? ? = 3 ∗ 0.866 ? ? = 1.5 ? ? = 2.598 ? ̅ = (?. ?, ?. ???) Realice analíticamente, las operaciones siguientes: ? ̅ − ? ̅ ? ̅ − ? ̅ = (1.5, 2.598) − (−1, 1.732) ? ̅ − ? ̅ = (1.5 − (−1), 2.598 − 1.732) ? ̅ − ? ̅ = (?. ?, ?. ???) |? − ?| = 2.5 2 + 0.866 2 |? − ?| = √6.25 + 0.7499 |? − ?| = √6.999 |? − ?| = ?. ???? tan 𝜃 = 0.866 2.5 tan 𝜃 = 0.3464 𝜃 = ?𝑎? −1 0.3464 𝜽 = ??. ??° 5?̅ − 2 ? ̅ 5? ̅ − 2 ? ̅ = 5(1.5 , 2.598) − 2(−1 , 1.732) 5? ̅ − 2 ? ̅ = (7.5 , 12.99) − (−2 , 3.464) 5? ̅ − 2 ? ̅ = (7.5 − (−2) , 12.99 − 3.464) ?? ̅ − ? ? ̅ = (?. ? , ?. ???)
|5?̅ − 2 ? ̅| = 9.5 2 + 9.526 2 |5?̅ − 2 ? ̅| = √90.25 + 90.7446 |5?̅ − 2 ? ̅| = √180.9946 |?? ̅ − ? ? ̅| = ??. ???? tan 𝜃 = 9.526 9.5 tan 𝜃 = 1.0027 𝜃 = ?𝑎? −1 1.0027 𝜽 = ??. ??° c. Encuentre el ángulo entre los siguientes vectores: ? ̅ = 2i + 9j y ? ̅ = -6i 4j ??? 𝜃 = (? ̅ ∗ ?̅) |? ̅| ∗ |?̅| |? ̅| = 2 2 + 9 2 |?̅| = √−6 2 + (−4) 2 |? ̅| = √4 + 81 |?̅| = √36 + 16 |? ̅| = √85 |?̅| = √52 |? ̅| = 9.219 |?̅| = 7.211 (? ̅ ∗ ?) ̅̅̅ = (2 , 9) ∗ (−6 ∗ −4) (? ̅ ∗ ?) ̅̅̅ = (2 ∗ −6 ) + (9 ∗ −4) (? ̅ ∗ ?) ̅̅̅ = −12 − 36 (? ̅ ∗ ?) ̅̅̅ = −48 ??? 𝜃 = −48 9.219 ∗ 7.211 ??? 𝜃 = −48 66.47 ??? 𝜃 = −0.722 𝜃 = ??? −1 − 0.722

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