Download App

The plane — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsThe plane3 Marks
Question
Determine the value of $\lambda$ for which the following planes are perpendicular to other.
$3\text{x}-6\text{y}-2\text{z}=7$ and $2\text{x}+\text{y}-\lambda\text{z}=5$
✓

Answer

We know that the planes $a_1x + b_1y + c_1z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$ are perperndicular to each other only if
$a_1a_2 + b_1b_2 + c_1c_2= 0$
The given planes are 3x - 6y - 2z = 7 and $2\text{x}+\text{y}-\lambda\text{z}=5$
$\Rightarrow a_1 = 3; b_1 = -6; c_1 = -2; a_2 = 2; b_2 = 1$; $\text{c}_2=-\lambda$
It is given that the given planes are perpendicular.
$\Rightarrow a_1a_2 + b_1b_2 + c_1c_2 = 0$
$\Rightarrow(3)(2)+(-6)(1)+(-2)(-\lambda)=0$
$\Rightarrow6-6+2\lambda=0$
$\Rightarrow2\lambda=0$
$\Rightarrow\lambda=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from The plane→The plane — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the inverse of each of the following matrices $($if they exist$) : \left[\begin{array}{ll}1 & -1 \\ 2 & 3\end{array}\right]$
→
Evaluate the following integrals:$\int\frac{1}{\sqrt{16-6\text{x}-\text{x}^2}}\text{ dx}$
→
With usual notations prove that $2\left\{a \sin ^2 \frac{C}{2}+c \sin ^2 \frac{A}{2}\right\}=a-b+c$.
→
Evaluate the following intregals:
$\int\frac{1}{(\text{x}-1)(\text{x}+1)(\text{x}+2)}\ \text{dx}$
→
Evaluate:
$\int\frac{\text{e}^{\log\sqrt{\text{x}}}}{\text{x}}\text{dx}$
→
If $\bar{a}, \bar{b}, \bar{c}$ are non coplanar vectors, then show that the four points $2 \bar{a}+\bar{b}, \bar{a}+2 \bar{b}+\bar{c}, 4 \bar{a}-2 \bar{b}-\bar{c}$ and $3 \bar{a}+4 \bar{b}-5 \bar{c}$ are coplanar.
→
Integrate the following functions w.r.t. x:

$\sin (\log x)$

→
On the set Z of integers a binary operation * is defined by a * b = ab + 1 for all a, b ∈ Z. Prove that * is not associative on Z.
→
Evaluate the following integrals:
$\int\frac{\text{x}\sin^{-1}\text{x}}{\sqrt{1-\text{x}^2}}\text{dx}$
→
In roulette, Figure, the wheel has 13 numbers 0, 1, 2,...., 12 maked on equally spaced slots. A player sets Rs 10 on a given number. He recieves Rs 100 from the organiser of the game if the ball comes to rest in this slot; otherwise he gets nothing. If X denotes the players net gain/loss, Find E(X).
→