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Question

Vector A has magnitude of 3 units and makes an angle of 30 with the positive x-axis.

Vector B has magnitude of 4 units and makes an angle of 120 with the positive x-axis.

Find the magnitude of the resultant and the angle that it makes with the positive x-axis.

[tan1(43)=53]


A

Angle =

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B

Angle =

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C

Angle =

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D

Angle =

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Solution

The correct option is C

Angle =


Given |A| = 3

|B| = 4

Magnitude of Resultant will be |R| = |A|2+|B|2+2|A||B|cosθ

Where θ is the angle between vector A & vector Bθ = 120 - 30 = 90

|R|=(3)2+(4)2+2.3.4.cos90

|R|=9+16+2.3.4.0 = 5

So , magnitude of resultant is 5

Now tan θ = |B|sinθ|A|+|B|cosθ

=4sin903+4cos90

tan ϕ=43

ϕ=tan1(43)=53

Caution : - But this ϕ is the angle that the resultant makes with the A vector and the question has asked about the angle that the resultant makes with the x - axis so it will be 53+30=83


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