$\"\"$

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

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consider $\"\"$ and $\"\"$ .

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Find the value of the $\"\"$ , when the two lines are intersect to each other.

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Equate the two line equations.

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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Consider $\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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The both functions have a slope of zero at $\"\"$ .

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Hence the two functions have the same angle at $\"\"$ .

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$\"\"$

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The slopes of the two lines are $\"\"$ and $\"\"$ .

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$

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Susbtitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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Hence the two vectros are $\"\"$ and $\"\"$ .

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

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The magnitude of $\"\"$ is $\"\"$

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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 angle is $\"\"$ at $\"\"$ .

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Therefore, the acute angle between the two curves at the point of intersection is $\"\"$ at $\"\"$ and $\"\"$ at $\"\"$ .

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$\"\"$

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The acute angle between two curves is $\"\"$ at $\"\"$ .