Question

What angle does a vector make with the positive x-axis if it has a component of 80 units on the negative x-axis and 60 units on the positive y-axis?

• A. ${30}^{\circ }$
• B. ${53}^{\circ }$
• C. ${37}^{\circ }$
• D. ${143}^{\circ }$

Answer 1

The correct option is D

${143}^{\circ }$

Translating the vector so as to be able to use triangle law

Given a right triangle using Pythagoras theorem we get hypotenuse or the resultant as 100 units (also resultant = $\sqrt{x^2+y^2}$) and angle that it makes with the 80 unit vector is $\theta$ and whose $tan\left(\theta \right)$ can be found using basic geometry.

$tan\theta =\frac{60}{80}=\frac{3}{4}={37}^{\circ }$ (also $\theta =ta{n}^{-1}\left(\frac{y}{x}\right)$) will give you the same answer) but here the resultant is

making an angle of ${37}^{\circ }$ with the 80 unit vector which itself is along the negative x-axis. so the angle that it makes with the positive x axis is ${180}^{\circ }$ - 37 = ${143}^{\circ }$