Question

The x-component of the resultant of several vectors :-
(a) Is equal to the sum of the x-components of the vectors
(b) May be smaller than the sum of the magnitudes of the vectors
(c) May be greater than the sum of the magnitudes of the vectors
(d) May be equal to the sum of the magnitudes of the vectors

• A. a, c, d
• B. a, b, c
• C. a, b, d
• D. b, c, d

Answer 1

The correct option is C a, b, d

We assume here two vectors , $\overrightarrow{a}=x_1\hat{i}+y_1\hat{j}+z_1\hat{k}$ and $\overrightarrow{b}=x_2\hat{i}+y_2\hat{j}+z_2\hat{k}$

The resultant, $\overrightarrow{r}=\overrightarrow{a}+\overrightarrow{b}=(x_1+x_2)\hat{i}+(y_1+y_2)\hat{j}+(z_1+z_2)\hat{k}$

Here we see that the x-component of the resultant is equal to the sum of the x-components of the vectors.

The magnitude of each vectors include $x,y$ and $z$ term but the $x$-component of it will include $x$ term only. So it may be smaller than the sum of magnitudes of vectors.

If all vectors only have $x$-component, then it may be equal to sum of the magnitudes of the vectors.