A vector p of magnitude 2 acting in x-y plane is making an angle 30' with positive x-axis. The vector P will be ​

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Answers 2

Answer:

√3 i^ + j^

Explanation:

In x axis = 2cos30° i^ = 2× √3/2 i^ = √3 i^

In y axis = 2sin 30° j^ = 2× 1/2 j^ = j^

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]

To know more about vectors please visit:

https://brainly.in/question/4959928

https://brainly.in/question/5067454

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