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Question
explain with the help of example what is the range of possible values of resultant of two vectors.

Answer
Hello muhammad,

When an airplane is flying in wind, the velocity with respect to the ground is the vector sum of the plane's airspeed (with direction, so you could call it airvelocity) and the wind's velocity. Suppose the plane wants to go east and the wind is blowing from the west. The plane is going eastward through the air and that air is going eastward. So the magnitude of the plane's velocity with respect to the ground is the algebraic sum of the 2 magnitudes, and the direction is eastward.

If the plane wants to go west, and the wind is still blowing from the west, the magnitude of the plane's velocity with respect to the ground is the algebraic difference between the 2 magnitudes, and the direction is westward (if the wind is really strong, or the plane is extremely slow, it could conceivably be going east).

If the plane wants to go north (and points his nose to the north) and the wind is blowing from the west, the magnitude of the resultant will be between the sum and the difference of the magnitudes of the 2 vectors. The direction will depend of the relative strengths of the airspeed and wind speed, but will be some angle in the 90 degrees between east and north.

In general: The range of the magnitude of the resultant could be from a-b to a+b where a and b are the magnitudes of the 2 vectors. The direction could be any point of the compass.

I hope this helps,
Steve

Physics

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Steve Johnson

Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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