Help with Physics Problem - Vector Addition & Subtraction

[degsclarit]

guy! I'am newbie here hope i will find some good friend .


guys, i homework in physics ,but i don't understand the question can anybody help me.

this is the question.

1. Considering graphical and analytical methods for obtaining the resultant, which method is more accurate? Give the probable sources of errors from which method.



2. Would the magnitude of the resultant be different for vector subtraction than for vector addition in each case? If so, state the whether the subtractive resultant would be greater than the additive resultan

can anyone help me...

 

[negitron]

Those questions are meaningless without the example they refer to.

 

[RoyalCat]

Those questions are meaningless without the example they refer to.

Well, the first one is pretty meaningless, since all the graphical approaches I know for calculating vector sums (Measuring with a ruler and protractor aside) are in essence analytical (Law of Cosines)

But as far as the second one goes, that does have an answer.

Consider the following vectors:

$$\vec r_1+\vec r_2=\vec r_3$$
Let's break them down into their axial components:
$$\vec r_1=r_{1_x}\hat x + r_{1_y}\hat y$$
$$\vec r_2=r_{2_x}\hat x + r_{2_y}\hat y$$

So the vector sum,
$$\vec r_3=(r_{1_x}+r_{2_x})\hat x+(r_{1_y}+r_{2_y})\hat y$$

Let's have a look at the definition of a vector's magnitude:
$$|r_3|\equiv\sqrt{r_{3_x}^2+r_{3_y}^2}$$

Now what you should do is look at what happens when you do vector subtraction as opposed to addition, and see how that affects the magnitude of the resultant vector, $$|r_3|$$