L3 : Angle between two lines - Straight line, Mathematics, Class 11 Video Lecture - Class 11 | Best Video for Class 11

hello friends this video straight line
sparked rays brought to you by exam fear
calm no more fear from exam before
watching this video please make sure
that you have watch straight lines part
1 & 2 now let's understand angles
between two lengths so if we had to find
the angle between two lines then we can
say tan theta is equal to m2 minus MN by
1 plus M very simple really nothing here
if this is alpha 2 this will become 180
minus alpha 2 correct because this is
straight line this is theta so this also
becomes theta vertical angles will add
all this angles of this triangle what we
get alpha 1 plus theta plus 180 minus
alpha 2 is equal to 180 degree correct
180 180 cancel so what we get is theta
is nothing but alpha 2 minus alpha 1
this is our first equation theta is
equal to 1 4 2 minus similarly let us
find Phi we can find Phi also so Phi is
equal to 180 degree minus theta phi is
equal to 180 degree minus theta this is
a straight line this is Theta this is
this specifying theta plus 5 into my ID
so we can say Phi is equal to 180 minus
theta these two equation here so if we
consider these two lines L 1 and L 2
they make two angles one angle is Theta
if you take this side and the other
angle is Phi this angle also theta and
this is the angular also Phi so we can
say there are two distinct angles made
by these two lines so what our answer
will be tan theta so we can say the
angle between these two lines will be
either tan theta or tan Phi
the other two angles made by these two
line so now we have to find time T time
ten so from Equation 1 we have theta is
equal to 5 minus PI 1 or we can say tan
theta is equal to 10 of Phi 2 minus 5
and this is going to tan of Phi 2 alpha
2 minus tan of alpha 1 by 1 plus tan of
alpha 1 into tan of alpha T we have read
this into my chapter this is 1 this is 2
tan of alpha 2 minus sine of alpha 1 by
1 plus tan of alpha 1 into everybody so
now we can say that tan of alpha 2 is
nothing but M 2 slope of line 2 tan upon
hormones nothing but ml and this is
again M this is tan of theta now
similarly we have to find tan of Phi is
nothing but tan of 180 degree minus
theta
why like this because Phi is good to 180
minus TDS we say tan of Phi is good to
tan operating minus theta this is
nothing but minus of tan theta so we
know that it is minus tan theta so it is
nothing with minus of M 2 minus M by 1
plus M so we have theta is either
I mean dying of between the lengths two
lines either M 2 minus MN by 1 plus M 2
M 1 M 2 or minus of M 2 minus M by 1 1
plus connected so we can write a general
equation that tan theta it can be a
Makita theta or Phi is equal to mod of M
2 minus M by
one plus M
please note mod is important here this
is the value they take one example of
angle between lines the question says if
angle between two lines is PI by four
and the slope of one line is one by two
find the slope of other line let me draw
the lines now this is one line this is
one line so we have two nights let's
suppose this slope is equal to 1 by 2
and this slope is M dash not given then
the angle between these neither bye-bye
so we have to find out none so we know
already know that tan of theta is
nothing but mod of M 1 minus M 2 by 1
plus M 1 correct
so or we can say it Teta is go to PI by
4 so we are told that tan of Phi by 4 is
nothing but mod of we'll say this is M
dash M dash minus 1 by 2 is M who will
say this is 1 plus M into 1 by LC m -
because here M - and has been to 1 by 2
this is M 2 or this is Emerson
correct now this is mod and tan PI by 4
is equal to 1 right if you remove the
word what we get is 2 condition that is
either M dash minus 1 by 2 by 1 plus M
dash by 2 is equal to 1 or M dash minus
1 by 2 by 1 plus M dash by 2 is equal to
minus 1 since we remove the mod so this
is either minus 1
plus one so we have two K's here so
we'll solve this case first so this
become M dash minus 1 by 2 is equal to 1
plus M dash by or we get M dash by 2 is
equal to 1 plus 1 by 2 it is 3 by 2 or
we get M dash is equal to 3 this is the
first part second part will do here so
here we'll hit M dash minus 1 by 2 plus
1 plus M dash by 2 is equal to 0 so this
is minus 1 this will become minus of
this will add this ticket here so this
becomes 3 M dash by 2 is equal to minus
1 by 2 or M Dash is equal to minus 1 by
so we have two values of address that is
3 or minus 1 by 3 so the slope of other
line is either 3 or minus 1 by 3 this is
the answer the slope of the other line
that is M dash is equal to 3 or minus 1
by 3 very simple what we have done we
have just use the formula tan theta is
equal to mod please no mod is very
crucial here tan theta is equal to mod
of M 1 minus M 2 by 1 plus M then M 2 we
have used theta is equal to PI by 4 M 2
is equal to 1 by 2 and we have solved to
get em - so we got to wherever by naps
and there's equal to 3 or minus 1 by 3
one more point to note here is when you
remove mod you say this is well 2 plus 1
or minus 1 so in this first one so it we
get plus 1 or minus 1 let me move on i
RH is become plus 1 n minus or plus the
value and minus the other in this
question we are asked to find the angle
between line 1 and line 2 so you want to
find the angle let's find the slope so
let's convert this into slow form first
equation we can say Y is equal to minus
root 3 X minus plus 5 so
the slope for migration is of this form
y is equal to MX plus C if you compare
this with this we get M is equal to
three first or second equation we have
root three Y is equal to X minus six we
have put in this fashion will divided by
root three whole equations left hand
side decade side work so we get Y is
equal to minus 1 by root three also plus
1 by root 3 X minus 6 Y so here this ml
this is M 2 so here M 2 is nothing but
plus 1 by root 3 so we have got slopes
of both the line what we have done we
have just converted with the general
form flying into normal form to get the
slopes so he found a slope of first line
is root 3 that is equation 1 the slope
of second line is 1 by unity now we have
to find the angle people these two
nights we know that if they are two
lines this is m1 and this is m2 and this
is the angle theta theta between these
hanging lines so we know that tan theta
is nothing but or temp i evan is nothing
Byrd mod of M 2 minus M 1 by 1 plus M 1
M 2 please don't mod is very Fischer
here because we are talking what we can
consider this Phi or this theta we can
take any angle so this mod is very
important here so this becomes mod of 1
by root 3 minus root 3 by 1 plus root 3
into 1 by root 3 what you get here is if
you solve this this becomes 1 minus 3 by
root 3 by 1 plus 1 so this becomes more
of this this becomes
post evaluating so this becomes we solve
this mod of minus 2 by root 3 by 2 2 2
cancel this becomes 1 by root 3 this is
the value we got tan theta is equal to 1
by 3 and we know that tan of 30 degree
is equal to 1 by root 3 so you can say
that effect is a mod of this mod of
little G so that does go to this is case
1 they are two case case 1 tan theta T
does equal to 1 by root 3 and K is 2 is
and theta is equal to minus under root
we have to kiss actually root 3 of em -
of a root 3 so in first case when you
say tan theta is equal to 1 by root 3 we
get theta is equal to 30 degree in this
case when you say tan it has been 2 - in
my 2 trees we get theta has been to 150
degree this is mod here so we have 2
guests and theta is equal to plus 1 by
root 2 your tan theta is equal to minus
1 by root 3 es tan theta has been 2 plus
1 by root 3 we get 3 Tasman fertility in
case tan theta is equal to minus 1 by
root 3 we get theta is equal to money
so what we have done here we have found
the slope of both the equations we have
used the formula tan theta is going to
mod please note more is important mod of
M 2 minus ml by 1 plus ml into we get
the value as mod of 1 by root 3 so we
got two cases case 1 and the desk will -
1 by root 3 K is 2 times 8 is equal to
minus 1 by root 3 we solved both the
cases to get them answer thank you
visit exam viacom to watch free
educational videos try free online tests
in the best quality study materials
study from the best tutors and mentors
and much more thanks again