$\"\"$

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The points are $\"\"$ and $\"\"$ .

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Consider the points of the line as $\"\"$ and $\"\"$ .

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Line segment through the two points is same as component vector of those two points.

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Component vector of $\"\"$ and $\"\"$ is represented as $\"\"$ .

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Line segment through the points $\"\"$ and $\"\"$ is represented as $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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The points are $\"\"$ and $\"\"$ .

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Consider the points of the line as $\"\"$ and $\"\"$ .

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Line segment through the points $\"\"$ and $\"\"$ is represented as $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Two vectors $\"\"$ and $\"\"$ are parallel if and only if $\"\"$ .

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Find the cross product of $\"\"$ and $\"\"$ .

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$\"\"$

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Since $\"\"$ , the lines $\"\"$ and $\"\"$ are parallel to each other.

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$\"\"$

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The lines are parallel to each other.