Question

Can we add 2 vectors of unequal magnitudes and get a zero vector?

• A. True
• B. False

Answer 1

The correct option is B

False

Let's assume my vector 1 is $x\hat{i}+y\hat{j}$. Now what vector should I add to it to get 0 vectors?

Let's say vector 2 be $u\hat{i}+v\hat{j}$

So vector 1+vector 2 = 0

$\Rightarrow x\hat{i}+y\hat{j}+u\hat{i}+v\hat{j}=0$

$\Rightarrow (x+u)\hat{i}+(y+v)\hat{j}=0$

$\Rightarrow x+u=0$

u = -x

Similarly, y + v = 0

v = -y

So my vector 2 is

$-x\hat{i}-y\hat{j}$

Let's see what's its magnitude is

$|\overrightarrow{\text{vector 2}}|=\sqrt{(-x{)}^2+(-y{)}^2}$

=$\sqrt{x^2+y^2}$

Wow so we find that magnitude of vector 1 is same as vector 2. So no it's not possible to have 2 vectors of unequal magnitude and get zero vector.