Let α, β, γ, δ be real numbers such that α^2+β^2+γ^2≠0 and α+γ=1. Suppose the point 3,2,-1 is the mirror image of the point 1,0,-1 with respect to the…

Question

Let α, β, γ, δ be real numbers such that α^2+β^2+γ^2≠0 and α+γ=1. Suppose the point 3,2,-1 is the mirror image of the point 1,0,-1 with respect to the plane αx+βy+γz=δ. Then which of the following statements is/are TRUE?

MARKS Content Team · Accepted Answer

Correct answer: (A) α+β=2; (B) δ-γ=3; (C) δ+β=4. From the diagram, Mid point of A & A' lies on the plane, i.e., B2,1,-1 2α+β-γ=δ…1 α+γ=1 ….2 Direction Ratio of AA^(')2,2,0 will be proportional to normal to the plane, (α)/2=(β)/2=(γ)/0=λ α=2λ, β=2λ, γ=0 ∴2λ+0=1 ⇒λ=1/2 ∴α=1, β=1, γ=0, δ=3 Now, (A) α+β+γ=1+1+0=2≠δ (B) α+β=1+1=2 (C) δ+β=3+1=4 (D) δ-γ=3

Let $α, β, γ, δ$ be real numbers such that $α^{2} + β^{2} + γ^{2} \neq 0$ and $α + γ = 1$ . Suppose the point $(3, 2, - 1)$ is the mirror image of the point $(1, 0, - 1)$ with respect to the plane $α x + β y + γ z = δ$ . Then which of the following statements is/are TRUE?

Solution

Relevant Questions

Let α, β, γ, δ be real numbers such that α2+β2+γ2≠0 and α+γ=1. Suppose the point 3,2,-1 is the mirror image of the point 1,0,-1 with respect to the plane αx+βy+γz=δ. Then which of the following statements is/are TRUE?

Solution

Relevant Questions

Let $α, β, γ, δ$ be real numbers such that $α^{2} + β^{2} + γ^{2} \neq 0$ and $α + γ = 1$ . Suppose the point $(3, 2, - 1)$ is the mirror image of the point $(1, 0, - 1)$ with respect to the plane $α x + β y + γ z = δ$ . Then which of the following statements is/are TRUE?