The plane 2x-(1- )y+3 =0 passes through the intersection of the p… - Vidyadip

MCQ

The plane $2\text{x}-(1-\lambda)\text{y}+3\lambda\text{z}=0$ passes through the intersection of the planes:

✓
2x - y = 0 and y- 3z = 0
B
2x + 3z = 0 and y = 0
C
2x - y + 3z = 0 and y - 3z = 0
D
None of these

✓

Answer

Correct option: A.

2x - y = 0 and y- 3z = 0

The given plane is

$2\text{x}-(1-\lambda)\text{y}+3\lambda\text{z}=0$

$\Rightarrow(2\text{x}-\text{y})+\lambda(-\text{y}+3\text{z})=0$

So, this plane passes through the intersection of the planes

2x - y = 0 and -y + 3z = 0

⇒ 2x - y = 0 and y - 3z = 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 "M.C.Q (1 Marks)" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

How many values of $k $ , systeam of linear equations $\left( {k + 1} \right)x + 8y = 4k\;,\;kx + \left( {k + 3} \right)y$$ = 3k - 1$ has no solutions.

A force $(\overrightarrow F ) = 2i + j - k$ acts at a point $A$, whose position vector is $2i - j$. The moment of $F$ about the origin is

The solution of the differential equation, $\frac{{dy}}{{dx}} = \frac{{y\,\, - \,\,x}}{{y\,\, - \,\,x\,\, - \,\,1}} ,$ given $y (- 5) = - 5$ represents

Let $\vec u\;$be a vector coplanar with the vector $\vec a = 2\hat i + 3\hat j - \hat k$ and $\vec b = \hat j + \hat k$ . If $\vec u$ is perpendicular to $\vec a$ and $\vec u \cdot \vec b = 24$ ,then ${\left| {\vec u} \right|^2} = $ . . . .

If A and B are two events such that $\text{P(A)}=\frac{1}{2},\text{P(B)}=\frac{1}{3},\text{P}(\text{A}|\text{B})=\frac{1}{4},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals.

The value of $\left| {\,\begin{array}{*{20}{c}}{{1^2}}&{{2^2}}&{{3^2}}\\{{2^2}}&{{3^2}}&{{4^2}}\\{{3^2}}&{{4^2}}&{{5^2}}\end{array}\,} \right|$ is

If a function $f(x)$ is increasing in an interval $x \in [a,b]$, then which of the following will always be correct -

Choose the correct answer from the given four options.

$\text{X}$	$1$	$2$	$3$	$4$
$\text{P}(\text{X})$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

For the following probability distribution $E(X^2)$ is equal to:

If $y = {x^{({x^x})}}$, then ${{dy} \over {dx}} = $

The cosines of the angle between any two diagonals of a cube is: