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

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

`\begin{gathered} \vec{a}=\langle√(40)*\left(\right.-(√(3))/(2)),√(40)*(1)/(2)\rangle \\ =\langle-(√(40)*√(3))/(2),(√(40))/(2)\rangle \\ =\langle-\sqrt{(40*3)/(4)},\sqrt{(40)/(4)}\rangle \\ =\langle-√(10*3),√(10)\rangle \end{gathered}`

Hence, the component form of a is given by:

`\vec{a}=\langle-√(30),√(10)\rangle`

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