Question
What are components of a vector?

Answer

$1.$ The given vector can be written as sum of two or more vectors along certain fixed directions. The vectors into which the given single vector is splitted are called components of the vector.
$2.$ Let $\overrightarrow{ A }= A _1 \hat{\alpha}+ A _2 \hat{\beta}+ A _3 \hat{\gamma}$ where, $\hat{\alpha}, \hat{\beta}$ and $\hat{\gamma}$ are unit vectors along chosen directions. Then, $A_1, A_2$ and $A_3$ are known as components of $\overrightarrow{ A }$ along three directions $\hat{\alpha}, \hat{\beta}$ and $\hat{\gamma}$.
$3.$ It two vectors are equal then, their corresponding components are also equal and vice$-$versa.
If $\vec{A}=\vec{B}$
i.e., if $A_x \hat{i}+A_y \hat{j}+A_z \hat{k}=B_x \hat{i}+B_y \hat{j}+B_z \hat{k}$, then $A_x=B_x, A_y=B_y$ and $A_z=B_z$
$[$Note: The magnitude of a vector is a scalar while each component of a vector is always a vector.$]$

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