Answer: (b). [tex]\sqrt{3} i+j[/tex]
Given: Magnitude of P , P=2
Angle with x-axis , θ=30
To find: Vector P
Explanation:
A vector quantity has both magnitude and direction. Displacement, velocity, acceleration and force are some examples of vectors.
We can resolve any vector in two dimension into 2 components.The components of a vector depict the influence of that vector in a given direction.
For an example, vector P in x-y plane can be resolved Into two components. An x-component and y-component. Let Pₓ and Py are called x and y components of vector respectively.And [tex]i[/tex] and [tex]j[/tex] are the unit vectors along x and y direction.
Then vector P can be represented as P = Pₓ [tex]i[/tex] + Py [tex]j[/tex]
Using simple trigonometry we can represent Pₓ and Py interms of magnitude of P and the angle that P makes with x axis.
We get
Pₓ= P cos θ
Py = P sin θ
Substituting these in our equationof P we get
P= P cosθ [tex]i[/tex] + P sinθ [tex]j[/tex]
Here magnitude of P is given P = 2
Angle θ - 30
Substituting these
[tex]P=2cos30 i+ 2 sin 30j[/tex]
[tex]P=2*(\sqrt{3} /2)i+ 2*(1/2)j[/tex]
[tex]P=\sqrt{3} i+j[/tex]
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