CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Perpendicular Form of a Straight Line

If two lines ...

Question

If two lines perpendicular to each other always satisfy the condition $cot θ_{1} + cot θ_{2} = 2,$ where $θ_{1}$ and $θ_{2}$ are the angles made by the lines with positive direction of $X -$ axis and $M_{1},$ $M_{2}$ be the respective slopes, then $∣ ∣ M_{1} + \sqrt{2} M_{2} ∣ ∣$ is equal to
(where $M_{1} > M_{2}$ )

Open in App

Solution

$\frac{1}{M_{1}} + \frac{1}{M_{2}} = 2 \Rightarrow M_{1} + M_{2} = - 2 (∵ M_{1} M_{2} = - 1) \Rightarrow M_{1} - \frac{1}{M_{1}} = - 2 \Rightarrow M_{1}^{2} + 2 M_{1} - 1 = 0 \Rightarrow M_{1} = - 1 \pm \sqrt{2} ∴ M_{1} = \sqrt{2} - 1, M_{2} = - \sqrt{2} - 1 (∵ M_{1} > M_{2})$

$∴ | M_{1} + \sqrt{2} M_{2} | = 3$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If two lines perpendicular to each other always satisfy the condition

cot θ_{1} + cot θ_{2} = 2,

θ_{1}

θ_{2}

are the angles made by the lines with positive direction of

X -

M_{1}, M_{2}

be the respective slope, then

| M_{1} + \sqrt{2} M_{2} |

is equal to
(where

M_{1} > M_{2}

Q. If two lines having slopes

m_{1}

m_{2}

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

If two lines have direction cosines

$l_{1}, m_{1}, n_{1}$ and $l_{2}, m_{2}, n_{2}$

then the condition for these lines being perpendicular to each other would be -

m₁ and m₂ are the slope of two perpendicular lines, if

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

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Straight Line

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Perpendicular Form of a Straight Line

Standard XIII Mathematics

Join BYJU'S Learning Program

CrossIcon