Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If the D. C’s of a line are $open parentheses fraction numerator text 1 end text over denominator text c end text end fraction comma fraction numerator text 1 end text over denominator text c end text end fraction comma fraction numerator text 1 end text over denominator text c end text end fraction close parentheses$ then c is equal to

$\pm 1$
$\pm 2$
$\pm \sqrt{3}$
$\pm \sqrt{2}$

hint Hint:

We are given the direction cosines of a line. Direction cosines are values of cosines a line makes with all three axis. The direction cosine contains a variable. We have to find the value of the variable. We will use the properties of direction cosines to find the answer.

The correct answer is: $plus-or-minus square root of 3$

The given direction cosines are as follows $1 over c comma 1 over c comma 1 over c$
We will use the properties of direction cosines to find the answer.
The direction cosines are generally denoted by l, m and n.
The sum of the square of the direction cosines is 1.
l²+ m² + n² = 1
We will substitute the values.
$open parentheses 1 over c close parentheses squared space plus space open parentheses 1 over c close parentheses squared space plus open parentheses 1 over c close parentheses squared equals space 1 1 over c squared plus space 1 over c squared space plus space 1 over c squared equals 1 T h e space d e n o m i n a t o r space i s space s a m e W e space c a n space a d d space t h e space n u m e r a t o r s fraction numerator 1 space plus space 1 space plus space 1 over denominator c squared end fraction equals 1 space space space space space space space space space space space space 3 over c squared equals 1 M u l t i p l y i n g space b o t h space t h e space s i d e s space b y space c squared space space space space space space space space space space space space space space space 3 space equals space c squared R e a r r a n i n g space t h e space e q u a t i o n space space space space space space space space space space space space space space c squared space equals space 3 T a k i n g space t h e space s q u a r e space r o o t space space space space space space space space space space space space space space c space equals space plus-or-minus square root of 3$
This is the value of c.

For such questions, we should know the properties of direction cosines.

Related Questions to study

The value of f(0) , so that the function $f left parenthesis x right parenthesis equals fraction numerator square root of a squared minus a x plus x squared end root minus square root of a squared plus a x plus x squared end root over denominator square root of a plus x end root minus square root of a minus x end root end fraction$ becomes continuous for all $x$ is given by

The value of f(0) , so that the function $f left parenthesis x right parenthesis equals fraction numerator square root of a squared minus a x plus x squared end root minus square root of a squared plus a x plus x squared end root over denominator square root of a plus x end root minus square root of a minus x end root end fraction$ becomes continuous for all $x$ is given by

Let f, g: R $not stretchy rightwards arrow$ R be two functions defined by $f open parentheses x close parentheses equals open curly brackets table row cell x s i n open parentheses fraction numerator 1 over denominator x end fraction close parentheses comma blank end cell row cell 0 blank comma end cell end table table row cell x blank not equal to 0 end cell row cell x equals 0 end cell end table close blank$ and g(x) = x f(x)
Statement 1: f is a continuous function at x = 0
Statement 2: g is a differentiable function at x = 0

Let f, g: R $not stretchy rightwards arrow$ R be two functions defined by $f open parentheses x close parentheses equals open curly brackets table row cell x s i n open parentheses fraction numerator 1 over denominator x end fraction close parentheses comma blank end cell row cell 0 blank comma end cell end table table row cell x blank not equal to 0 end cell row cell x equals 0 end cell end table close blank$ and g(x) = x f(x)
Statement 1: f is a continuous function at x = 0
Statement 2: g is a differentiable function at x = 0

lf $f left parenthesis theta right parenthesis equals open vertical bar table row 1 cell c o s theta end cell 1 row cell negative s i n theta end cell 1 cell negative c o s theta end cell row cell negative 1 end cell cell s i n theta end cell 1 end table close vertical bar$ $negative 12$ x2 and A and 8 are respecively the maximum and the minimum values of $left parenthesis theta right parenthesis$ , then (A, B) is equal to

lf $f left parenthesis theta right parenthesis equals open vertical bar table row 1 cell c o s theta end cell 1 row cell negative s i n theta end cell 1 cell negative c o s theta end cell row cell negative 1 end cell cell s i n theta end cell 1 end table close vertical bar$ $negative 12$ x2 and A and 8 are respecively the maximum and the minimum values of $left parenthesis theta right parenthesis$ , then (A, B) is equal to

parallel

Binding energy pernucleonversus mass number curve for nuclei is shown in the figure. W,X,Y and Z are fournuclei indicate don the curve.Theprocessthatwouldrelease

Binding energy pernucleonversus mass number curve for nuclei is shown in the figure. W,X,Y and Z are fournuclei indicate don the curve.Theprocessthatwouldrelease

Physics-General

Which of the plots shown in the figure represents speed(vn) of the electron in a hydrogen atom as a function of theprincipalquantumnumber(n)?

Which of the plots shown in the figure represents speed(vn) of the electron in a hydrogen atom as a function of theprincipalquantumnumber(n)?

Physics-General

lf the Rolle’s theorem holds for the function $f left parenthesis x right parenthesis equals 2 x cubed plus a x squared plus b x$ in the interval [−1, 1] for the point $c equals fraction numerator 1 over denominator 2 end fraction$ , then the value of 2a+b is

lf the Rolle’s theorem holds for the function $f left parenthesis x right parenthesis equals 2 x cubed plus a x squared plus b x$ in the interval [−1, 1] for the point $c equals fraction numerator 1 over denominator 2 end fraction$ , then the value of 2a+b is

parallel

If $u subscript 1 end subscript$ is the frequency of the series limit of Lymanseries, $u subscript 2 end subscript$ is the frequency of the firstline of Lymanseries and
u₃ is the frequency of the series limit of the Balmer seriesthen

If $u subscript 1 end subscript$ is the frequency of the series limit of Lymanseries, $u subscript 2 end subscript$ is the frequency of the firstline of Lymanseries and
u₃ is the frequency of the series limit of the Balmer seriesthen

Physics-General

The diagram shows the energy levels for an electron in acertainatom. Which transitionshown represents theemissionofaphotonwiththemostenergy?

The diagram shows the energy levels for an electron in acertainatom. Which transitionshown represents theemissionofaphotonwiththemostenergy?

Physics-General

Thestopping potential $open parentheses V subscript 0 end subscript close parentheses$ , versus frequency(v) plotofasubstance is
shown in figure, the threshold wavelengthis

Thestopping potential $open parentheses V subscript 0 end subscript close parentheses$ , versus frequency(v) plotofasubstance is
shown in figure, the threshold wavelengthis

Physics-General

parallel

Thefigureshowsaplotofphotocurrentversusanodepotentialforaphotosensitivesurfaceforthreedifferent radiations.Whichoneofthefollowingisacorrectstatement?

Thefigureshowsaplotofphotocurrentversusanodepotentialforaphotosensitivesurfaceforthreedifferent radiations.Whichoneofthefollowingisacorrectstatement?

Physics-General

Lightofwavelength500nmisincidentonametalwithwork function2.28 eV. The de Broglie wavelengthof the emittedelectronis:

Lightofwavelength500nmisincidentonametalwithwork function2.28 eV. The de Broglie wavelengthof the emittedelectronis:

Physics-General

In an experiment on photoelectric effect, a student plotsstoppingpotentialVO against reciprocalof the wavelength $lambda$ oftheincidentlightfortwodifferentmetalsAandB.Theseareshown inthefigure.

Looking atthegraphs,youcanmostappropriatelysaythat

In an experiment on photoelectric effect, a student plotsstoppingpotentialVO against reciprocalof the wavelength $lambda$ oftheincidentlightfortwodifferentmetalsAandB.Theseareshown inthefigure.

Looking atthegraphs,youcanmostappropriatelysaythat

Physics-General

parallel

Twoinsulatingplatesarebothuniformlychargedinsuchawaythatthepotentialdifferencebetweenthemis $V subscript 2 end subscript$ - $V subscript 1 end subscript$ =20V.(i.e.,plate2isatahigherpotential).The plates are separatedby d =0.1mand canbe treatedasinfinitelylarge.Anelectronisreleasedfromrestontheinner surfaceofplate1.Whatisitsspeedwhenithitsplate2?

Twoinsulatingplatesarebothuniformlychargedinsuchawaythatthepotentialdifferencebetweenthemis $V subscript 2 end subscript$ - $V subscript 1 end subscript$ =20V.(i.e.,plate2isatahigherpotential).The plates are separatedby d =0.1mand canbe treatedasinfinitelylarge.Anelectronisreleasedfromrestontheinner surfaceofplate1.Whatisitsspeedwhenithitsplate2?

Physics-General

Photoelectric effect experiments are performed using three different metal plates $p comma q$ and $r$ having work functions $ϕ subscript p end subscript equals 2.0 e V comma ϕ subscript q end subscript equals 2.5 e V$ and $ϕ subscript r end subscript equals 3.0 e V$ , respectively. A light beam containing wavelengths of $550 text end text n m comma 450 text end text n m$ and $350 text end text n m$ with equal intensities illuminates each of the plates. The correct $I minus V$ graph for the experiment is:
(Take hc $equals 1240 e V n m$ )

Photoelectric effect experiments are performed using three different metal plates $p comma q$ and $r$ having work functions $ϕ subscript p end subscript equals 2.0 e V comma ϕ subscript q end subscript equals 2.5 e V$ and $ϕ subscript r end subscript equals 3.0 e V$ , respectively. A light beam containing wavelengths of $550 text end text n m comma 450 text end text n m$ and $350 text end text n m$ with equal intensities illuminates each of the plates. The correct $I minus V$ graph for the experiment is:
(Take hc $equals 1240 e V n m$ )

Physics-General

Let f be differentiable for all x. if f(1) = -2 and $f to the power of ´ end exponent open parentheses x close parentheses greater or equal than 2$ for x $element of$ [1,6], then

Let f be differentiable for all x. if f(1) = -2 and $f to the power of ´ end exponent open parentheses x close parentheses greater or equal than 2$ for x $element of$ [1,6], then

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.