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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

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B

53

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C

37

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D

143

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Solution

The correct option is D

143


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 = x2+y2) and angle that it makes with the 80 unit vector is θ and whose tan(θ) can be found using basic geometry.

tanθ=6080=34=37 (also θ=tan1(yx)) will give you the same answer) but here the resultant is

making an angle of 37 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 - 37 = 143


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