Let the equation of the plane containing the straight line x - 1-2 - y - 2-3 - z-5 are perpendicular to the plane x - y - z - 2 - 0 be kx - ny - z - 4 - m- Find k-n -

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

Byju's Answer

Standard XII

Mathematics

Equation of Perpendicular from a Point on a Line

Let the equat...

Question

Let the equation of the plane containing the straight line $\frac{x - 1}{2} = \frac{y + 2}{- 3} = \frac{z}{5}$ are perpendicular to the plane $x - y + z + 2 = 0$ be $k x + n y + z + 4 = m$ . Find $k + n$ ?

Open in App

Solution

Line : $\frac{x - 1}{2} = \frac{y + 2}{- 3} = \frac{z}{5}$
Plane : $x - y + z + 2 = 0$
The vector perpendicular to required plane is
$∣ ∣ ∣ ∣ \begin{matrix} i & j & k 2 & - 3 & 5 1 & - 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 2 i + 3 j + k$
Now equation of plane passing through $(1, - 2, 0)$ and perpendicular to $2^i + 3^j +^k$ is given by,
$(x - 1) 2 + (y + 2) 3 + (z - 0) 1 = 0$
$\Rightarrow 2 x + 3 y + z + 4 = 0$
On comparing with the equation $k x + n y + z + 4$ , we have $k = 2, n = 3$ .
Therefore, $k + n = 2 + 3 = 5$
Ans: 5

Suggest Corrections

Similar questions

Q. The equation of the plane containing the straight line

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

and perpendicular to the plane

x - y + z + 2 = 0

Q. The equation of the plane containing the straight line

\frac{x}{2} = \frac{y}{3} = \frac{z}{4}

and perpendicular to the plane containing the straight lines

\frac{x}{3} = \frac{y}{4} = \frac{z}{2} and \frac{x}{4} = \frac{y}{2} = \frac{z}{3}

is :

Q. Let the equation of the plane which contains the line

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

and which is perpendicular to the plane

2 x + 7 y - 3 z = 1.

k x - m y - z + p = 0.

Find

p - k - m

Q. Equation of the plane containing the straight line

\frac{x}{2} = \frac{y}{3} = \frac{z}{4}

and perpendicular to the plane containing the straight lines

\frac{x}{3} = \frac{y}{4} = \frac{z}{2}

and

\frac{x}{4} = \frac{y}{2} = \frac{z}{3}

Equation of the plane containing the straight line $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ and perpendicular to the plane containing the staight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2}$ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3}$ is

Join BYJU'S Learning Program

Let the equation of the plane containing the straight line x−12=y+2−3=z5 are perpendicular to the plane x−y+z+2=0 be kx+ny+z+4=m. Find k+n ?

Let the equation of the plane containing the straight line $\frac{x - 1}{2} = \frac{y + 2}{- 3} = \frac{z}{5}$ are perpendicular to the plane $x - y + z + 2 = 0$ be $k x + n y + z + 4 = m$ . Find $k + n$ ?