The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle \pi /4 with plane x+y=3  are

  • Option 1)

    1,\sqrt{2},1

  • Option 2)

    1,1,\sqrt{2}

  • Option 3)

    1,1,2

  • Option 4)

    \sqrt{2},1,1

 

Answers (1)

As we learnt in 

Direction Ratios -

If l,m,n are direction cosines then three numbers a,b,c propotional to l,m,n are called direction cosines. 

a=kl,b=km,c=kn

 

-

 

 Plane through (1,0,0) is 

a(x-1)+by +cz= 0

It passes though (0,1,0) 

We get, -a +b =0

\Rightarrow a=b

\cos 45^{0}= \frac{a+a}{\sqrt{2(2a^{2}+c^{2})}}

\Rightarrow c= \sqrt{2}a

DRs of normal are (a,a, \sqrt{2}a)

(1,1, \sqrt{2})

 


Option 1)

1,\sqrt{2},1

Incorrect option

Option 2)

1,1,\sqrt{2}

Correct option

Option 3)

1,1,2

Incorrect option

Option 4)

\sqrt{2},1,1

Incorrect option

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