If the system of linear equations. 8 x+y+4 z=-2 x+y+z=0 λ x-3 y=μ has infinitely many solutions, then the distance of the point (λ, μ,-(1/2)) from the plane 8 x + y +4 z +2=0 is :

Question

If the system of linear equations. 8 x+y+4 z=-2 x+y+z=0 λ x-3 y=μ has infinitely many solutions, then the distance of the point (λ, μ,-(1/2)) from the plane 8 x + y +4 z +2=0 is : (A) 3 √5 (B) 4 (C) (26/9) (D) (10/3)

Tardigrade Admin · Accepted Answer

D = | 8 1 4 1 1 1 λ -3 0|=0 ⇒ λ=4 Also D 1= D 2= D 3=0 So μ=-2 Point (4,-2,-(1/2)) Distance from plane =(10/3)

Q. If the system of linear equations.
$8 x + y + 4 z = - 2$
$x + y + z = 0$
$λ x - 3 y = μ$
has infinitely many solutions, then the distance of the point $(λ, μ, - \frac{1}{2})$ from the plane $8 x + y + 4 z + 2 = 0$ is :

$35$

4

$\frac{26}{9}$

$\frac{10}{3}$

$D = ∣ ∣ 81 λ 11 - 3 410 ∣ ∣ = 0 \Rightarrow λ = 4$
Also $D_{1} = D_{2} = D_{3} = 0$
So $μ = - 2$
Point $(4, - 2, - \frac{1}{2})$
Distance from plane $= \frac{10}{3}$

Q. If the system of linear equations. 8x+y+4z=−2 x+y+z=0 λx−3y=μ has infinitely many solutions, then the distance of the point (λ,μ,−21​) from the plane 8x+y+4z+2=0 is :

35​

4

926​

310​

D=∣∣​81λ​11−3​410​∣∣​=0⇒λ=4 Also D1​=D2​=D3​=0 So μ=−2 Point (4,−2,−21​) Distance from plane =310​

Q. If the system of linear equations.
$8 x + y + 4 z = - 2$
$x + y + z = 0$
$λ x - 3 y = μ$
has infinitely many solutions, then the distance of the point $(λ, μ, - \frac{1}{2})$ from the plane $8 x + y + 4 z + 2 = 0$ is :

$35$

$\frac{26}{9}$

$\frac{10}{3}$

$D = ∣ ∣ 81 λ 11 - 3 410 ∣ ∣ = 0 \Rightarrow λ = 4$
Also $D_{1} = D_{2} = D_{3} = 0$
So $μ = - 2$
Point $(4, - 2, - \frac{1}{2})$
Distance from plane $= \frac{10}{3}$