Consider a plane P:2x+y-z=5, a line L:(x-3)/2=(y+1)/(-3)=(z-2)/(-1) and a point A3,-4,1. If the line L intersects plane P at B and the xy plane at C…

Question

Consider a plane P:2x+y-z=5, a line L:(x-3)/2=(y+1)/(-3)=(z-2)/(-1) and a point A3,-4,1. If the line L intersects plane P at B and the xy plane at C, then the area (in sq. units) of ∆ABC is

MARKS Content Team · Accepted Answer

Correct answer: (C) √10. For xy plane, putting z=0, we get, (x-3)/2=(y+1)/(-3)=2⇒x=7,y=-7 Coordinates of point C are 7,-7,0 Any general point on the line is 2λ+3,-3λ-1,-λ+2 This must satisfy the given plane 4λ+6-3λ-1+λ-2=5 2λ+3=5⇒λ=1 So, coordinates of point B are 5,-4,1 AB→=<2,0,0>AC→=<4,-3,-1> Area =1/2AB→×AC→=1/2 i^ j^ k^ 2 0 0 4 -3 -1 =1/2-2-j^+3k^=j^-3k^=√10 sq. units

Consider a plane $P : 2 x + y - z = 5$ , a line $L : \frac{x - 3}{2} = \frac{y + 1}{- 3} = \frac{z - 2}{- 1}$ and a point $A (3, - 4,1)$ . If the line $L$ intersects plane $P$ at $B$ and the $x y$ plane at $C$ , then the area (in sq. units) of $∆ A B C$ is

Solution

More Three Dimensional Geometry Questions

Consider a plane P:2x+y-z=5, a line L:x-32=y+1-3=z-2-1 and a point A3,-4,1. If the line L intersects plane P at B and the xy plane at C, then the area (in sq. units) of ∆ABC is

Solution

More Three Dimensional Geometry Questions

Consider a plane $P : 2 x + y - z = 5$ , a line $L : \frac{x - 3}{2} = \frac{y + 1}{- 3} = \frac{z - 2}{- 1}$ and a point $A (3, - 4,1)$ . If the line $L$ intersects plane $P$ at $B$ and the $x y$ plane at $C$ , then the area (in sq. units) of $∆ A B C$ is