Question

obtain an expression for magnitude
of force

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Answer 1

Answer:

Using the x and y coordinates for the components, this gives F = √(x2 + y2) for the magnitude of the force. Find the resultant force from two vectors by first adding the x-components and y-components to find the resultant vector and then use the same formula for its magnitude.

Explanation:

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Answer 2

Explanation:

Let P and Q be two vectors acting simultaneously at a point and represented both in magnitude and direction by two adjacent sides OA and OD of a parallelogram OABD as shown in figure.

Let θ be the angle between P and Q and R be the resultant vector. Then, according to parallelogram law of vector addition, diagonal OB represents the resultant of P and Q.

So, we have

                R = P + Q

Now, expand A to C and draw BC perpendicular to OC.

From triangle OCB,

   

In triangle ABC,

   

Also,

   

Magnitude of resultant:

Substituting value of AC and BC in (i), we get

   

which is the magnitude of resultant.

Direction of resultant: Let ø be the angle made by resultant R with P. Then,

From triangle OBC,

   

which is the direction of resultant.

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