Question

obtain the equation for rectangular components of a vector in a plane​

Answer 1

Answer:

There are majorly two types of quantities, scalar and vector quantities. All the quantities are divided into these two categories. Scalar quantities are those quantities, which have only magnitude eg – mass, speed, pressure, etc. Vector quantities are those which have both magnitude and directions eg – weight, velocity and thrust. The special fact about vectors is that we can resolve it into components.

Complete step by step answer:

Rectangular components means the components or parts of a vector in any two mutually perpendicular axes. This could be understood by an example as illustrated below.

Let a vector quantity ‘R’ inclined at an angle $\theta$ from the x-axis. By convention, we can split the vector ‘R’ in two rectangular components. As shown in the figure, the vector ‘R’ is split into two components;

$R_x$along x-axis and $R_y$ along y-axis. This is an extremely important and useful property of vectors. Using it, we can solve complex problems very easily. Also, we can write the values of these components as;

$R_x = Rcos\theta$

$R_y=Rsin\theta$

Additional Information: For any two general vectors, we have the magnitude of their resultant $R = \sqrt{A^2+B^2+2ABcos\theta}$. Since we have split the given vector ‘R’ into two independent vectors, we can see that doing this won't change the magnitude of the original vector.

Here A = $R_x = Rcos\theta$ and B = $R_y=Rsin\theta$

Hence, putting in the formula:

$R = \sqrt{A^2+B^2+2ABcos\theta}$

$\Rightarrow R = \sqrt{(Rcos\theta)^2+(Rsin\theta)^2+2(Rcos\theta)(Rsin\theta)cos90^{\circ}}$

As $cos\ 90^{\circ} = 0$

$R = \sqrt{R^2[(cos\theta)^2+(sin\theta)^2]+0}$

Also, $sin^2\theta+cos^2\theta = 1$

So, $R = \sqrt{R^2} = R$

Hence proved.

Answer 2

Answer:

1.Obtain expression for rectangular components.

2.The figure illustrates a vector represented by . ...

3.The vector is the resolved part of along the X – axis. ...

4.Applying the law of triangle of vectors to ONP, = + or = + , which also confirm that Ax, Ay are the components of A. ...

5.⇒ Ax = A cosθ … ( ...

6.⇒ Ax = A sinθ … ( ...

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