Advertisements
Advertisements
Question
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is ______.
Solution
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is `x/"a" + y/"b" + z/"c"` = 1.
Explanation:
Given points are (2, 0, 0), (0, 3, 0) and (0, 0, 4).
So, the intercepts cut by the plane on the axes are 2, 3, 4
Equation of the plane (intercept form) is `x/"a" + y/"b" + z/"c"` = 1
⇒ `x/2 + y/3 + z/4` = 1
APPEARS IN
RELATED QUESTIONS
Write the sum of intercepts cut off by the plane `vecr.(2hati+hatj-k)-5=0` on the three axes
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`
Write the equation of the plane whose intercepts on the coordinate axes are 2, −3 and 4.
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
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 with intercept 3 on the y-axis and parallel to the ZOX plane.
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 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 \[\vec{r} \cdot \left( 5 \hat{i} + 3 \hat{j} - 6 \hat{k} \right) + 8 = 0 .\]
Find the equation of the plane passing through the intersection of the planes \[\vec{r} \cdot \left( 2 \hat{i} + \hat{j} + 3 \hat{k} \right) = 7, \vec{r} \cdot \left( 2 \hat{i} + 5 \hat{j} + 3 \hat{k} \right) = 9\] and the point (2, 1, 3).
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 vector equation of the plane through the line of intersection of the planes x + y+ z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x − y + z = 0.
Find the vector equation of the plane passing through the intersection of the planes
\[\vec{r} \cdot \left( \hat{ i } + \hat{ j }+ \hat{ k }\right) = \text{ 6 and }\vec{r} \cdot \left( \text{ 2 } \hat{ i} +\text{ 3 } \hat{ j } + \text{ 4 } \hat{ k } \right) = - 5\] and the point (1, 1, 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 equation of the plane through the line of intersection of the planes \[x + y + z =\]1 and 2x \[+\] 3 \[+\] y \[+\] 4\[z =\] 5 and twice of its \[y\] -intercept is equal to three times its \[z\]-intercept
Find the length of the perpendicular from origin to the plane `vecr. (3i - 4j-12hatk)+39 = 0`
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.
The intercepts made by the plane 2x – 3y + 5z + 4 = 0 on the coordinate axes are `-2, 4/3, (-4)/5`.
The equation of the plane which is parallel to 2x − 3y + z = 0 and which passes through (1, −1, 2) is:
