Question

Vector a is expressed in magnitude and direction form as a = ⟨√40 , 150∘⟩What is the component form a?

Answer 1

The component form of a is given by:

$\vec{a}=\langle\sqrt{40}\cos(150^{^{\circ}}),\sqrt{40}\sin(150^{^{\circ}})\rangle$$\vec{a}=\langle\sqrt{40}\cos(150^{^{\circ}}),\sqrt{40}\sin(150^{^{\circ}})\rangle$

Substitute cos (150°) = -√3/2 and sin (150°) = 1/2 into the equation:

$\begin{gathered} \vec{a}=\langle\sqrt{40}\times\left(\right.-\frac{\sqrt{3}}{2}),\sqrt{40}\times\frac{1}{2}\rangle \\ =\langle-\frac{\sqrt{40}\times\sqrt{3}}{2},\frac{\sqrt{40}}{2}\rangle \\ =\langle-\sqrt{\frac{40\times3}{4}},\sqrt{\frac{40}{4}}\rangle \\ =\langle-\sqrt{10\times3},\sqrt{10}\rangle \end{gathered}$

Hence, the component form of a is given by:

$\vec{a}=\langle-\sqrt{30},\sqrt{10}\rangle$

Therefore, the component form of vector a is given by ⟨-√30 , √10⟩