[العز2009]

السلام عليكم ورحمة الله وبركاته
يا اخوان ممكن احد يحل هذا المثال


Tow vector, the magnitude of the first is 6 units and the magnitude of the other 9 units, the angle between them is:
1) 30 degree 2) 60 degree 3) 90 degree 4) 150 degree 5) 180 degree
Find the resultant in each case and its direction with respect to the small vector

[Einstein Uae]

بسم الله الرحمن الرحيم

وعليكم السلام ورحمة الله وبركاته

مـا أعرف كثير للمتجهات بس بحاول وإن شاء يكون صحيح .. راح أحل أول بارت وباخذ الزاوية 30 ..

بسم الله


a) First of all lets call Vector A = 6 Units , Vector B = 9 Units , Angle between them is 30 Degrees Celsius.

The resultant of these two vectors denoted as A+B.

So to find the magnitude of A+B = √ ( A^2 + B^2 + 2AB cos30) = 14.5097

This is the magnitude & it is done and finished.

Now to find the direction with respect the smaller vector which is obviously A we have to use this equation to find alpha

tan α = B sin30 / (A + B cos 30) = 0.3262

Then α = 18.07

this is the angle between the resultant A+B and A .

So the resultant makes an angle of 18.07 degrees with vector A.