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Introduction to LOCI

Let L 1 and L...

Question

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

A

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B

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C

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D

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Solution

The correct option is B

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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}

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}

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

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

.

(l_{1}, m_{1}, n_{1})

(l_{2}, m_{2}, n_{2})

are d.c's two lines. Then
The lines are perpendicular if

l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} = 0

(l_{1}, m_{1}, n_{1})

(l_{2}, m_{2}, n_{2})

are d.c's two lines. Then
The lines are parallel is

\frac{l_{1}}{l_{2}} = \frac{m_{1}}{m_{2}} = \frac{n_{1}}{n_{2}}

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 -

Q. If two lines with direction cosines

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

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

intersect, then the angle between them would be -

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