Advertisements
Advertisements
प्रश्न
Write the equation of the plane whose intercepts on the coordinate axes are 2, −3 and 4.
उत्तर
\[\text{ We know that the equation of the plane with a, b and c intercepts on the coordianate axes is given by } \]
\[\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1\]
\[\text{ Given that } \]
\[a = 2; b = - 3; c = 4\]
\[\text{ So, the equation of the required plane is } \]
\[\frac{x}{2} + \frac{y}{- 3} + \frac{z}{4} = 1\]
\[ \Rightarrow 6x - 4y + 3z = 12\]
APPEARS IN
संबंधित प्रश्न
Find the intercepts cut off by the plane 2x + y – z = 5.
Prove that if a plane has the intercepts a, b, c and is at a distance of P units from the origin, then `1/a^2 + 1/b^2 + 1/c^2 = 1/p^2`
A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is `1/x^2 + 1/y^2 + 1/z^2 = 1/p^2`
if z = x + iy, `w = (2 -iz)/(2z - i)` and |w| = 1. Find the locus of z and illustrate it in the Argand Plane.
Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes.
4x + 3y − 6z − 12 = 0
Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes.
2x + 3y − z = 6
Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes.
2x − y + z = 5
Find the equation of a plane which meets the axes at A, B and C, given that the centroid of the triangle ABC is the point (α, β, γ).
Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts on the coordinate axes.
Find the equation of the plane with intercept 3 on the y-axis and parallel to the ZOX plane.
Find the equation of the plane through the point \[2 \hat{i} + \hat{j} - \hat{k} \] and passing through the line of intersection of the planes \[\vec{r} \cdot \left( \hat{i} + 3 \hat{j} - \hat{k} \right) = 0 \text{ and } \vec{r} \cdot \left( \hat{j} + 2 \hat{k} \right) = 0 .\]
Find the equation of the plane passing through the line of intersection of the planes 2x − y = 0 and 3z − y = 0 and perpendicular to the plane 4x + 5y − 3z = 8
Find the equation of the plane which contains the line of intersection of the planes x + 2y + 3z − 4 = 0 and 2x + y − z + 5 = 0 and which is perpendicular to the plane 5x + 3y − 6z+ 8 = 0.
Find the equation of the plane through the line of intersection of the planes x + 2y + 3z + 4 = 0 and x − y + z + 3 = 0 and passing through the origin.
Find the vector equation (in scalar product form) of the plane containing the line of intersection of the planes x − 3y + 2z − 5 = 0 and 2x − y + 3z − 1 = 0 and passing through (1, −2, 3).
Find the equation of the plane that is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z − 4 = 0, 2x + y − z + 5 = 0.
Find the equation of the plane passing through the intersection of the planes 2x + 3y − z+ 1 = 0 and x + y − 2z + 3 = 0 and perpendicular to the plane 3x − y − 2z − 4 = 0.
Find the equation of the plane through the line of intersection of the planes \[\vec{r} \cdot \left( \hat{i} + 3 \hat{j} \right) + 6 = 0 \text{ and } \vec{r} \cdot \left( 3 \hat{i} - \hat{j} - 4 \hat{k} \right) = 0,\] which is at a unit distance from the origin.
Find the equation of the plane that contains the line of intersection of the planes \[\vec{r} \cdot \left( \hat{i} + 2 \hat{j} + 3 \hat{k} \right) - 4 = 0 \text{ and } \vec{r} \cdot \left( 2 \hat{i} + \hat{j} - \hat{k} \right) + 5 = 0\] and which is perpendicular to the plane \[\vec{r} \cdot \left( 5 \hat{i} + 3 \hat{j} - 6 \hat{k} \right) + 8 = 0 .\]
A plane makes intercepts −6, 3, 4 respectively on the coordinate axes. Find the length of the perpendicular from the origin on it.
Find the equation of the plane through the intersection of the planes 3x − y + 2z = 4 and x + y + z = 2 and the point (2, 2, 1).
Find the equation of the plane which contains the line of intersection of the planes x \[+\] 2y \[+\] 3 \[z - \] 4 \[=\] 0 and 2 \[x + y - z\] \[+\] 5 \[=\] 0 and whose x-intercept is twice its z-intercept. Hence, write the equation of the plane passing through the point (2, 3, \[-\] 1) and parallel to the plane obtained above.
Find the locus of a complex number, z = x + iy, satisfying the relation `|[ z -3i}/{z +3i]| ≤ sqrt2 `. Illustrate the locus of z in the Argand plane.
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is ______.
The equation of the plane which is parallel to 2x − 3y + z = 0 and which passes through (1, −1, 2) is:
