If the three planes $x = 5, 2 x - 5 a y + 3 z - 8 = 0$ and $3 b x + y - 3 z = 0$ contains a common line then (a,b) lies equal to

(\frac{- 1}{5} \frac{8}{15})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{1}{5} \frac{- 8}{15})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(\frac{- 8}{15} \frac{1}{5})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{8}{15} \frac{- 1}{5})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $(\frac{1}{5} \frac{- 8}{15})$
A] 3 planes are

$x = 5, 2 x - 5 a y + 3 z - 2 = 0, 3 b x + y - 3 z = 0$

substitute $x = 5$ in $2 x - 5 a y + 3 z - 2 = 0$

$= 2 (5) - 5 a y + 3 z - 2 = 0$

$= 10 - 5 a y + 3 z - 2 = 0$

$= 8 - 5 a y + 3 z = 0$ (1)

substitute $x = 5$ in $3 b x + y - 3 z = 0$

$= 3 b (5) + y - 3 z = 0$

$= 15 b + y - 3 z = 0$ (2)

as both contain a common line

$8 - 5 a y + 3 z = 0$

$15 b + y - 3 z = 0$

happens when

$5 a = + 1$ $15 b = - 8$

$a = + 1 / 5$ $b = - 8 / 15$

$∴ (a, b) = (\frac{1}{5}, \frac{- 8}{15})$

Suggest Corrections

Similar questions

Q. A plane

P

contains the line

x + 2 y + 3 z + 1 = 0 = x - y - z - 6,

and is perpendicular to the plane

- 2 x + y + z + 8 = 0.

Then which of the following points lies on

P ?

Q. The equation of the plane which contains the line

\frac{x}{4} = \frac{y}{2} = \frac{z}{1}

and is perpendicular to the plane containing the lines

\frac{x - 4}{1} = \frac{y - 5}{4} = \frac{z - 9}{2}

and

\frac{x + 8}{4} = \frac{y + 6}{2} = \frac{z - 2}{1}

Q. Equation of the plane containing the line

x + 2 y + 3 z - 4 = 0 = 2 x + y - z + 5

and perpendicular to the plane

5 x + 3 y - 6 z + 8 = 0

The distance of the point P (3,8,2) from the line $\frac{1}{2} (x - 1) = \frac{1}{4} (y - 3) = \frac{1}{3} (z - 2)$ measured parallel to the plane $3 x + 2 y - 2 z + 15 = 0 i s$

Q. If the line

\frac{x - 2}{3} = \frac{y - 1}{- 5} = \frac{z + 2}{2}

lies on the plane

x + 3 y - α z + β = 0

, then

(α, β)

equals .

Join BYJU'S Learning Program

If the three planes x=5, 2x−5ay+3z−8=0 and 3bx+y−3z=0 contains a common line then (a,b) lies equal to

If the three planes $x = 5, 2 x - 5 a y + 3 z - 8 = 0$ and $3 b x + y - 3 z = 0$ contains a common line then (a,b) lies equal to