કેટલાક સદિશોના પરિણામીનો x ઘટક.......(a) એ સદ | vedclass

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Question

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

Vedclass · Accepted Answer

$a, b, d$

Vedclass · Answer

We assume here two vectors, $\vec{a}=x_1 \hat{i}+y_1 \hat{j}+z_1 \hat{k}$ and $\vec{b}=x_2 \hat{i}+y_2 \hat{j}+z_2 \hat{k}$

The resultant, $\vec{r}=\vec{a}+\vec{b}=\left(x_1+x_2\right) \hat{1}+\left(y_1+y_2\right) \hat{j}+\left(z_1+z_2\right) \hat{k}$

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.

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