Trigonometric EquationMedium
Question
Equation of line in the plane π ≡ 2x - y + z - 4 = 0 which is perpendicular to the l whose equation is 
and which passes through the point of intersection of l and π is
and which passes through the point of intersection of l and π is Options
A.
B.
C.
D.
Solution
Let direction ratios of the line be a,b,c , then
2a - b + c = 0
a - b - 2c = 0
i.e.
∴ direction ratios of the line are 3,5,-1
Any point on the line is (2 + λ, 2 - λ, 3 - 2λ). It like on the plane π if
2(2 + λ) - (2 - λ) + (3 - 2λ) = 4
i.e. 4 + 2λ - 2 + λ + 3 - 2λ = 4
i.e λ = - 1
∴ The point of intersection of thye line and the plane is (1, 3, 5)
∴ equation of the required line is
2a - b + c = 0
a - b - 2c = 0
i.e.
∴ direction ratios of the line are 3,5,-1
Any point on the line is (2 + λ, 2 - λ, 3 - 2λ). It like on the plane π if
2(2 + λ) - (2 - λ) + (3 - 2λ) = 4
i.e. 4 + 2λ - 2 + λ + 3 - 2λ = 4
i.e λ = - 1
∴ The point of intersection of thye line and the plane is (1, 3, 5)
∴ equation of the required line is
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