$\"\"$

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Parametric equations of the lines are $\"\"$ and $\"\"$ .

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Standard form of parametric equations of the line are $\"\"$ , where vector $\"\"$ is parallel line to the line.

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Compare $\"\"$ with standard form.

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Parallel line corresponding to the line $\"\"$ is $\"\"$ .

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Consider $\"\"$ .

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Similarly parallel line corresponding to the line $\"\"$ is $\"\"$ .

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Consider $\"\"$ .

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If these two parallel lines $\"\"$ are parallel, then the lines $\"\"$ and $\"\"$ also parallel.

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The cross product of the two parallel lines is zero.

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

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$\"\"$

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Since the cross product is not equal to zero, then the lines are not parallel.

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$\"\"$

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Check for intersection of the lines:

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For point of intersection of $\"\"$ and $\"\"$ , find the point by solving the lines.

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$\"\"$

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$\"\"$

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Equate the corresponding components.

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$\"\"$

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$\"\"$

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$\"\"$

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Solve equations $\"\"$ and $\"\"$ to find the values of $\"\"$ and $\"\"$ .

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Multiply the equation $\"\"$ by $\"\"$ and $\"\"$ by $\"\"$ .

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$\"\"$

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$\"\"$

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Subtract the above equations.

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Thus, the values of $\"\"$ do not satisfy the equation $\"\"$ .

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Hence they are not intersecting lines.

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The lines $\"\"$ and $\"\"$ are not intersection lines, they are skew lines.

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$\"\"$

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The lines $\"\"$ and $\"\"$ are skew lines.