Question

The position vector ⃗r of a particle P located in an x-y plane is shown in figure. a)Redraw the figure by showing the rectangular components.
b)Write the position vector in terms of rectangular components.
c)Write an equation to find the magnitude of the resultant of 2 vectors A and B​

Answer 1

this is the answer

you can write as x and y or as cos and sin component

Answer 2

The position vectors in terms of rectangular components are: psinθ and pcosθ

The equation to find the magnitude is given by,

r = $\sqrt{p^2cos^2(theta)+p^2sin^2(theta)}$

• The planes are always split into two rectangular components namely sinθ and cosθ. The x-plane is named as cosθ and the y-plane is named as sinθ.
• ∴ x = cosθ and y = sinθ
• x-plane in vector form is called as i-component and y-plane in vector form is called as j-component.
• The Magnitude of both the components is r = $\sqrt{px^2+py^2}$  → (equation 1) on substituting the values of 'x' and 'y' in equation 1 we get,   r = $\sqrt{p^2cos^2(theta)+p^2sin^2(theta)}$ . Here 'r' is the position vector.