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  • I need help with - Three Dimensional Geometry - JEE Main-5

L_1 is line\frac{x}{1}=\frac{y}{2}=\frac{z}{3} and P_1 is plane 3x+6y-5z=0 then

  • Option 1)

    L_1 is parallel to plane, but not lying in the plane 

  • Option 2)

    L_1 is lieing in the plane completely

  • Option 3)

    L_1 and P_1 have one common point

  • Option 4)

    L_1 andP_1 intersect and angle \frac{\pi}{3}

 

Answers (1)

best_answer

As we have learned

Condition for line to be parallel to plane -

\vec{b}\cdot \vec{n}= 0 or a_{1}a+b_{1}b+c_{1}c= 0

-

 

 Here direction of line is \hat{i}+2\hat{j}+3\hat{k} and direction of normal to plane is 3\hat{i}+6\hat{j}-5\hat{k} and we see their dot product 3+12-15=0 It means line is perpendicular to normal to plane, so will be parallel to plane. But also, we see a point of line, let us take (0,0,0) also lies on plane so line completely lies in plane, because we see line and plane have one common point and both are parallel


Option 1)

L_1 is parallel to plane, but not lying in the plane 

Option 2)

L_1 is lieing in the plane completely

Option 3)

L_1 and P_1 have one common point

Option 4)

L_1 andP_1 intersect and angle \frac{\pi}{3}

Posted by

Himanshu

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