Let α,β,γ be three real numbers satisfying α β γ 2 -1 1 -1 -1 -2 -1 2 1 =0 0 0. If the point Aα,β,γ lies on the plane 2x+y+3z=2, then 3α+2β-6γ is…

Question

Let α,β,γ be three real numbers satisfying α β γ 2 -1 1 -1 -1 -2 -1 2 1 =0 0 0. If the point Aα,β,γ lies on the plane 2x+y+3z=2, then 3α+2β-6γ is equal to

MARKS Content Team · Accepted Answer

Correct answer: (B) -1/3. α β γ 2 -1 1 -1 -1 -2 -1 2 1 =0 0 0 2α-β-γ -α-β+2γ α-2β+γ =0 0 0 ⇒2α-β-γ=0 -α-β+2γ=0 α-2β+γ=0 Using cramer’s rule ∆= 2 -1 -1 -1 -1 2 1 -2 1 =2-1+4+1-1-2-12+1 =6-3-3=0 So, the system of equations has infinite solutions Put γ=k 2α-β=k α+β=2k ⇒γ=k,β=k ⇒α,β,γ≡k,k,k ∵α,β,γ satisfies 2x+y+3z=2 ⇒6k=2⇒k=1/3 α,β,γ≡1/3,1/3,1/3 ⇒3α+2β-6γ=-1/3

Let $α, β, γ$ be three real numbers satisfying $[α β γ] [\begin{matrix} 2 & - 1 & 1 \\ - 1 & - 1 & - 2 \\ - 1 & 2 & 1 \end{matrix}] = [0 0 0]$ . If the point $A (α, β, γ)$ lies on the plane $2 x + y + 3 z = 2$ , then $3 α + 2 β - 6 γ$ is equal to

Solution

More Matrices Questions

Let α,β,γ be three real numbers satisfying α β γ 2-1 1-1-1-2-1 2 1=0 0 0. If the point Aα,β,γ lies on the plane 2x+y+3z=2, then 3α+2β-6γ is equal to

Solution

More Matrices Questions

Let $α, β, γ$ be three real numbers satisfying $[α β γ] [\begin{matrix} 2 & - 1 & 1 \\ - 1 & - 1 & - 2 \\ - 1 & 2 & 1 \end{matrix}] = [0 0 0]$ . If the point $A (α, β, γ)$ lies on the plane $2 x + y + 3 z = 2$ , then $3 α + 2 β - 6 γ$ is equal to