Consider the line Lt 3 3t 4t 3t Then L is to the plane 45

Consider the line L(t) = (3 + 3t, - 4t, -3t). Then: L is to the plane 4.5x - 6y - 4.5z = 21 L is to the plane 3x + 4y - 5z = -4 L is to the plane 8y - 6x + 6z = 8 L is to the plane x - 4z = 8

Solution

Answer :

Consider the given Line L(t) = ( 3 + 3t , - 4t , - 3t)

This line can be written as L(t) = ( 3 , 0 , 0 ) + t( 3 , - 4 , - 3)

Now the plane 4.5x - 6y - 4.5z = 21 has normal vector paralle to ( 4.5 , - 6 , - 4.5 )

So the normal is ( 4.5 , - 6, - 4.5 ) = 1.5( 3 , - 4 , - 3 )

So this lune parallel to the plane