If a point P (α, β, γ) satisfying (α β γ) beginpmatrix 2 10 8 9 3 8 8 4 8 endpmatrix=(0 0 0) lies on the plane 2 x+4 y+3 z=5, then 6 α+9 β+7 γ is equal to :

Question

If a point P (α, β, &gamma;) satisfying (α β &gamma;) beginpmatrix 2 10 8 9 3 8 8 4 8 endpmatrix=(0 0 0) lies on the plane 2 x+4 y+3 z=5, then 6 α+9 β+7 &gamma; is equal to : (A) (5/4) (B) -1 (C) 11 (D) (11/5)

Tardigrade Admin · Accepted Answer

2 α+4 β+3 &gamma;=5 .........(1) 2 α+9 β+8 &gamma;=0 .........(2) 10 α+3 β+4 &gamma;=0 .........(3) 8 α+8 β+8 &gamma;=0.........(4) Subtract (4) from (2) -6 α+β=0 β=6 α.........(5) From equation (4) 8 α+48 α+8 &gamma;=0 &gamma;=-7 α.........(6) From equation (1) 2 α+24 α-21 α=5 5 α=5 α=1 β=+6, &gamma;=-7 ∴ 6 α+9 β+7 &gamma; =6+54-49 =11

Q. If a point $P (α, β, γ)$ satisfying
$(α β γ) ⎝ ⎛ 2981034888 ⎠ ⎞ = (000)$
lies on the plane $2 x + 4 y + 3 z = 5$ , then $6 α + 9 β + 7 γ$ is equal to :

$\frac{5}{4}$

$- 1$

11

$\frac{11}{5}$

Q. If a point P(α,β,γ) satisfying (αβγ)⎝⎛​298​1034​888​⎠⎞​=(000) lies on the plane 2x+4y+3z=5, then 6α+9β+7γ is equal to :

45​

−1

11

511​

Q. If a point $P (α, β, γ)$ satisfying
$(α β γ) ⎝ ⎛ 2981034888 ⎠ ⎞ = (000)$
lies on the plane $2 x + 4 y + 3 z = 5$ , then $6 α + 9 β + 7 γ$ is equal to :

$\frac{5}{4}$

$- 1$

$\frac{11}{5}$