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Consider a plane x+y-z=1 and the point A(1,2,-3) A line L has the equation x=1+3r y=2-r z=3+4r Equation of the plane containing the line L and the point A has the equation (A) x-3y+5 (B)x+3y-7=0 (C) 3x-y-1=0 (D)3x+y-5=0

Consider a plane
x+y-z=1 and the point A(1,2,-3)
 
A line L has the equation
x=1+3r
y=2-r
z=3+4r
 
Equation of the plane containing the line L and the point A has the equation
(A) x-3y+5
(B)x+3y-7=0
(C) 3x-y-1=0
(D)3x+y-5=0

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
Put any 2 values of r to get the coordinates of any 2 points that lie on the linegiven by
x=1+3r
y=2-r
z=3+4r
Let those points be B and C
So, we need to the eqn of a plane which contains 3 points A, B and C.
Use the condition of coplanarity of 3 points to find the eqn of the plane using the triple product as

[(\vec{r}-\vec{a}) (\vec{b}-\vec{a})(\vec{c}-\vec{a})]=0
Answer is option B

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