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  • I need help with - Three Dimensional Geometry - JEE Main-4

Angle between line \frac{x-1}{1}=\frac{y-1}{2}=\frac{z-1}{2} and plane 2x+2y-3z+1=0 is

  • Option 1)

    \frac{\pi}{3}

  • Option 2)

    \frac{\pi}{6}

  • Option 3)

    \frac{\pi}{2}

  • Option 4)

    0

 

Answers (1)

best_answer

As we have learned

Angle between line and Plane (Cartesian form ) -

The angle between a line and the  line

\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c} plane

a_{1}x+b_{1}y+c_{1}z+d=0 is given by

\sin \Theta = \frac{a_{1}a+b_{1}b+c_{1}c}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a^{2}+b^{2}+c^{2}}}

-

 

 Here, a=1,b=2,c=2 

and a_1=2,b_1=2,c_1=-3

sin\theta=\frac{2(1)+2(2)+(-3)(2)}{\sqrt{4+4+9}\sqrt{1+4+4}}=0

\Rightarrow \theta=0

 


Option 1)

\frac{\pi}{3}

Option 2)

\frac{\pi}{6}

Option 3)

\frac{\pi}{2}

Option 4)

0

Posted by

Himanshu

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