Answer to Question #178934 in Calculus for John withers

Question

Write the following 2-space vectors in Cartesian form:

a . | 𝑢⃗ | = 1 0 , 𝜃 = 6 0 °

b. |𝑣| = 8, 𝜃 = 135°

c. |𝑤⃗ | = 5, 𝜃 = 210°

Answer 1

a) Cartesian form is-

$x ucos\theta +uysin\theta$

$=10xcos60+10ysin60=5x+5\sqrt{3}y$

(b) Cartesian form is-

$x vcos\theta +vysin\theta$

$=8xcos135+8ysin135=\dfrac{x}{2}+\dfrac{\sqrt{3}y}{2}$

(c) Cartesian form is-

$x wcos\theta +wysin\theta$

$=5xcos210+5sin210=\dfrac{-5\sqrt{3}}{2}x-\dfrac{5}{2}y$