How will you get the resultant of all vectors?

Answer 1

Graphical Vector Addition

Draw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.

Or, to do it mathematically (with 2 vectors):

You have vector a with angle Ao, and vector b with angle Bo.

To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)

Example:

Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.

c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )

angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )