If $\overrightarrow A = 2\widehat i + 3\widehat j + 4\widehat k$ and $\overrightarrow B = \widehat i - \widehat j + \widehat k$,find their subtraction $\overrightarrow A - \overrightarrow B$ using the algebraic method.
To find the subtraction of two vectors $\overrightarrow A$ and $\overrightarrow B$,we subtract their corresponding components.
Given: $\overrightarrow A = 2\widehat i + 3\widehat j + 4\widehat k$ and $\overrightarrow B = \widehat i - \widehat j + \widehat k$.
The subtraction is defined as $\overrightarrow A - \overrightarrow B = (A_x - B_x)\widehat i + (A_y - B_y)\widehat j + (A_z - B_z)\widehat k$.
Substituting the values:
$\overrightarrow A - \overrightarrow B = (2 - 1)\widehat i + (3 - (-1))\widehat j + (4 - 1)\widehat k$.
$\overrightarrow A - \overrightarrow B = 1\widehat i + (3 + 1)\widehat j + 3\widehat k$.
$\overrightarrow A - \overrightarrow B = \widehat i + 4\widehat j + 3\widehat k$.
Given: $\overrightarrow A = 2\widehat i + 3\widehat j + 4\widehat k$ and $\overrightarrow B = \widehat i - \widehat j + \widehat k$.
The subtraction is defined as $\overrightarrow A - \overrightarrow B = (A_x - B_x)\widehat i + (A_y - B_y)\widehat j + (A_z - B_z)\widehat k$.
Substituting the values:
$\overrightarrow A - \overrightarrow B = (2 - 1)\widehat i + (3 - (-1))\widehat j + (4 - 1)\widehat k$.
$\overrightarrow A - \overrightarrow B = 1\widehat i + (3 + 1)\widehat j + 3\widehat k$.
$\overrightarrow A - \overrightarrow B = \widehat i + 4\widehat j + 3\widehat k$.
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