11. -/1 points details my notes scalcet9 12.2.029. the initial point of a vector v in r² is the origin and…
11. -/1 points details my notes scalcet9 12.2.029. the initial point of a vector v in r² is the origin and the terminal point is in quadrant ii. if v makes an angle 5π/6 with the positive x - axis and |v| = 8, find v in component form. v = need help? read it watch it submit answer
Answer
Explanation:
Step1: Usar fórmulas de componentes de vector
Si un vector $\mathbf{v}$ tiene magnitud $|\mathbf{v}| = r$ y forma un ángulo $\theta$ con el eje $x$-positivo, entonces sus componentes son dadas por $v_x=r\cos\theta$ y $v_y = r\sin\theta$. Aquí $r = 8$ y $\theta=\frac{5\pi}{6}$.
Step2: Calcular la componente $x$
$v_x=|\mathbf{v}|\cos\theta=8\cos\frac{5\pi}{6}$. Sabemos que $\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}$, entonces $v_x = 8\times(-\frac{\sqrt{3}}{2})=- 4\sqrt{3}$.
Step3: Calcular la componente $y$
$v_y=|\mathbf{v}|\sin\theta=8\sin\frac{5\pi}{6}$. Sabemos que $\sin\frac{5\pi}{6}=\frac{1}{2}$, entonces $v_y = 8\times\frac{1}{2}=4$.
Answer:
$\left\langle - 4\sqrt{3},4\right\rangle$