# 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) $(1,-2,-7)$

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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