The value of k such that the line x -4-1- y -2-1- z - k -2 lies on the plane 2 x -4 y - z -7 isA- -7B- 4C- -4D- 7

The correct option is D 7 nbsp; nbsp;Let x 4/1=y 2/1=z k/2=λ then x=λ +4, y=λ +2, z=2 λ+k Given, the line lies on the plane. ⇒ 2(λ +4) 4(λ +2)+2 λ+k =7 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Modulus

The value of ...

Question

The value of $k$ such that the line $\frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}$ lies on the plane $2 x - 4 y + z = 7$ is

- 7

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

4

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

- 4

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

7

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

Open in App

Solution

The correct option is D $7$
$Let \frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2} = λ$
$then x = λ + 4, y = λ + 2, z = 2 λ + k$
Given, the line lies on the plane.
$\Rightarrow 2 (λ + 4) - 4 (λ + 2) + 2 λ + k = 7$
$\Rightarrow k = 7$

Suggest Corrections

Similar questions

The value of
$k$ such that $\frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}$
lies in the plane $2 x - 4 y + z = 7$ is

Q. The value of k such that

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

lies in the plane 2x -4y +z =7, is

Q. The line

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

lies exactly in the plane

2 x - 4 y + z = 7

, then value of

k

Q. For what value of

^{'} k^{'}

the line

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

lies on the plane

2 x - y + z - 7 = 0

Q. The line

L_{1} : \frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}

lies in the plane

2 x - 4 y + z = 7

, then the equation of the plane containing the line

L_{1}

and perpendicular to the plane

2 x - 4 y + z = 7,

is:

Join BYJU'S Learning Program

The value of k such that the line x−41=y−21=z−k2 lies on the plane 2x−4y+z=7 is

The correct option is D 7 Let x−41=y−21=z−k2=λ then x=λ+4, y=λ+2, z=2λ+k Given, the line lies on the plane. ⇒2(λ+4)−4(λ+2)+2λ+k=7 ⇒k=7

The value of $k$ such that the line $\frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}$ lies on the plane $2 x - 4 y + z = 7$ is

The correct option is D $7$
$Let \frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2} = λ$
$then x = λ + 4, y = λ + 2, z = 2 λ + k$
Given, the line lies on the plane.
$\Rightarrow 2 (λ + 4) - 4 (λ + 2) + 2 λ + k = 7$
$\Rightarrow k = 7$