$\"\"$

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The two line equations are $\"\"$ and $\"\"$ .

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Find an acute angle between the two lines.

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Consider $\"\"$ .

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Solve for $\"\"$ .

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$\"\"$

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$\"\"$

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The vector form of line equation $\"\"$ is $\"\"$ .

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Consider $\"\"$ .

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Solve for $\"\"$ .

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$\"\"$ .

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The vector form of line equation $\"\"$ is $\"\"$ .

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The two vectors are $\"\"$ and $\"\"$ .

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The angle between the two vectors is $\"\"$ .

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The magnitude of the vector $\"\"$ is $\"\"$ .

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The magnitude of the vector $\"\"$ is $\"\"$ .

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$\"\"$

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The dot product of $\"\"$ and $\"\"$ is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The acute angle between the two lines is $\"\"$ .

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Therefore,the acute angle is $\"\"$ .

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$\"\"$

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The acute angle is $\"\"$ .