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Byju's Answer

Standard XII

Mathematics

Angle between Pair of Straight Lines

The acute ang...

Question

The acute angle $α$ between two straight lines having slopes $m_{1}$ and $m_{2}$ , is given by;
$t a n α = (\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣$

True

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False

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Solution

The correct option is A True

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Similar questions

Q. The acute angle

α

between two straight lines having slopes

m_{1}

and

m_{2}

, is given by;

t a n α = (\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣

Let L₁ and L₂ be two non-vertical lines with slopes m₁ and m₂ respectively. If α₁ and α₂ are the inclinations of lines L₁ and L₂, respectively. the acute angle (say θ) between lines L1 and L2 , is given by

Q. If

m_{1} & m_{2}

are the slopes of two intersecting lines

(m_{1} . m_{2} \neq - 1) & θ

is the acute angle between them, then

t a n θ = | \frac{m_{1} + m_{2}}{1 - m_{1} . m_{2}} |

Q. Assertion :The direction cosines of one of the angular bisectors of two intersecting lines having direction cosines as

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

are proportional to

l_{1} + l_{2}, m_{1} + m_{2}, n_{1} + n_{2}

. Reason: The angle between the two intersecting lines having direction cosines as

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

is given by

cos θ = l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2}

Q. If two lines having slopes

m_{1}

and

m_{2}

are parallel to each other, then which of the following is correct?

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The acute angle α between two straight lines having slopes m1 and m2, is given by; tan α=(m1−m21+m1m2∣∣

The correct option is A True

The acute angle $α$ between two straight lines having slopes $m_{1}$ and $m_{2}$ , is given by;
$t a n α = (\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣$