Question

let ( vec{p}=overrightarrow{g e} ) where ( e(0,5) ) and ( g(-4,-3) ). what is the direction angle of ( -\frac{1}{2} vec{p} ) ?
( 27^{circ} )
( 63^{circ} )
( 117^{circ} )
( 257^{circ} )

Explanation:

Step1: Find the vector \(\vec{p}\)

Given \(P(0,5)\) and \(Q(-4,-3)\), the vector \(\vec{p}=\langle x_2 - x_1,y_2 - y_1
angle=\langle-4 - 0,-3 - 5
angle=\langle-4,-8
angle\). Then \(-\frac{1}{2}\vec{p}=\langle2,4
angle\).

Step2: Use the formula for the direction angle \(\theta\)

The formula for the direction angle \(\theta\) of a vector \(\langle a,b
angle\) is \(\tan\theta=\frac{b}{a}\). For the vector \(\langle2,4
angle\), \(a = 2\) and \(b = 4\). So \(\tan\theta=\frac{4}{2}=2\).

Step3: Calculate the angle

\(\theta=\arctan(2)\approx63^{\circ}\) (using a calculator to find the arctangent value).

Answer:

\(63^{\circ}\)