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can some one explain to me what just happened? how can they just change the angle to 90 degrees? is it cus it wants min?
Yes, the minimum distance between a point an a line is the perpendicular distance.
In fact, this (minimum) distance is called the "distance of a point from a line", with the 90 degrees understood.
In the particular example, the distance represents the magnitude of the vector, hence the direction of the vector F2 is at 90 degrees with the horizontal.
Also, in the diagram, it gave various options other than 90 degrees, attempting to illustrate that all the other options do not give a minimum value (magnitude) for F2.
Ok so in other words when it says minimum and its talking about a vector the angle would ALWAYS be 90 degree?
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I cannot say "always" without seeing the problem.
In general, you need to consider each engineering problem individually, case by case, in order not to miss anything. The answer lies in engineering and mathematical principles.
However, in Euclidean space, the minimum distance of a point from a line is always at 90 degrees with the line, as explained above.