The point at which the line joining the points (2,-3,1) and (3,-4,-5) intersects the plane , 2x+y+z=7 is

  • Option 1)

    (-1,2,7))

  • Option 2)

    (1,-2,7)

  • Option 3)

    (1,2,7)

  • Option 4)

    (1,-2,-7)

 

Answers (1)
P Plabita

As we learnt in concept

Intersection of line and plane -

Let 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 intersect at P

to find P assume general point on line as \left ( x_{1}+\lambda a_{1}y_{1} +\lambda b_{1}z_{1}+\lambda c_{1}\right )

now put it in plane to find \lambda,

a_{1}\left ( x_{1}+\lambda a \right )+b_{1}\left ( y_{1}+\lambda b \right )+c_{1}\left ( z_{1}+\lambda c \right )+d=0

-

 

 x_{1}=2, y_{1}=-3, z_{1}=1

a=3-2=1, b=-4+3=-1, C=-5-1=-6

So point on line

(2+\lambda ,-3-\lambda , 1-6\lambda )

which line on plane

so,

2(2+\lambda )+(-3-\lambda )+(1-6\lambda )=7

=>-5\lambda =5

=>\lambda =-1

\therefore The point is (1,-2,7)


Option 1)

(-1,2,7))

Option is incorrect

Option 2)

(1,-2,7)

Option is correct

Option 3)

(1,2,7)

Option is incorrect

Option 4)

(1,-2,-7)

Option is incorrect

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