(B) The equation of any plane parallel to $5x - 6y + 7z = 3$ is of the form $5x - 6y + 7z = k$. Since this plane passes through the point $(2, 3, 4)$,

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(B) The equation of any plane parallel to $5x - 6y + 7z = 3$ is of the form $5x - 6y + 7z = k$. Since this plane passes through the point $(2, 3, 4)$,we substitute these coordinates into the equation: $5(2) - 6(3) + 7(4) = k$ $10 - 18 + 28 = k$ $20 = k$ Substituting the value of $k$ back into the equation,we get $5x - 6y + 7z = 20$,which can be written as $5x - 6y + 7z - 20 = 0$.

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY Plane

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The equation of the plane passing through $(2, 3, 4)$ and parallel to the plane $5x - 6y + 7z = 3$ is:

A
$5x - 6y + 7z + 20 = 0$
B
$5x - 6y + 7z - 20 = 0$
C
$-5x + 6y - 7z + 3 = 0$
D
$5x + 6y + 7z + 3 = 0$

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THREE DIMENSIONAL GEOMETRY

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Plane

$A$ variable plane is at a distance $k$ from the origin and meets the coordinate axes at $A, B, C$. The locus of the centroid of $\Delta ABC$ is . . . . . .

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The distance of the plane $2x - 3y + 6z + 14 = 0$ from the origin is:

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If planes $\vec{r} \cdot (p \hat{i} - \hat{j} + 2 \hat{k}) + 3 = 0$ and $\vec{r} \cdot (2 \hat{i} - p \hat{j} - \hat{k}) - 5 = 0$ include an angle $\frac{\pi}{3}$,then the value of $p$ is

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If $S$ is the set of all real values of $a$ such that a plane passing through the points $(-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2)$ also passes through the point $(-1, -1, 1)$,then $S=$

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The image of the point $(1, 2, -1)$ on the plane containing the line $\frac{x + 1}{-3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ and the point $(0, 7, -7)$ is:

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The equation of the plane passing through $(2, 3, 4)$ and parallel to the plane $5x - 6y + 7z = 3$ is:

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$A$ variable plane is at a distance $k$ from the origin and meets the coordinate axes at $A, B, C$. The locus of the centroid of $\Delta ABC$ is . . . . . .

The distance of the plane $2x - 3y + 6z + 14 = 0$ from the origin is:

If planes $\vec{r} \cdot (p \hat{i} - \hat{j} + 2 \hat{k}) + 3 = 0$ and $\vec{r} \cdot (2 \hat{i} - p \hat{j} - \hat{k}) - 5 = 0$ include an angle $\frac{\pi}{3}$,then the value of $p$ is

If $S$ is the set of all real values of $a$ such that a plane passing through the points $(-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2)$ also passes through the point $(-1, -1, 1)$,then $S=$

The image of the point $(1, 2, -1)$ on the plane containing the line $\frac{x + 1}{-3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ and the point $(0, 7, -7)$ is:

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