Get Answers to all your Questions

header-bg qa

Let L be the line of intersection of the planes 2x+3y+z=1\; \; and\; \; x+3y+2z=2. If L makes an angle \alpha with the positive x-axis,then \cos \alpha equals

  • Option 1)


  • Option 2)


  • Option 3)


  • Option 4)



Answers (1)

As we learnt in 

Direction Cosines -

i)    \sin^{2} \alpha+ \sin^{2} \beta+\sin^{2} \gamma= 2

ii)    If OP =r then the co-ordinates of P will be (lr,mr,nr)

iii)    Direction cosines of X-axis are (1,0,0)

iv)    Direction cosines of Y-axis are (0,1,0)

v)    Direction cosines of Z-axis are (0,0,1)



 Let DCs of L be (l,m,n) then 2l+3m+2n=0 and l + 3m + 2n = 0 

On solving


So,\: \: \: \: l:m:n= \frac{l}{\sqrt{}3},\frac{-1}{\sqrt3},\frac{1}{\sqrt3}

cos\alpha =\frac{1}{\sqrt{3}}

Option 1)


Incorrect Option


Option 2)


Incorrect Option


Option 3)


Correct Option


Option 4)


Incorrect Option


Posted by

Sabhrant Ambastha

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE