Advertisements
Advertisements
प्रश्न
उत्तर
The given plane is 2x + y - x = 5
Dividing both sides of the equation by 5, we obtain
`2/5"x" + "y"/5 - "z"/5 = 1`
⇒ `"x"/(5/2) + "y"/5 + "z"/(-5) = 1`
It is known that the equation of a plane in intercept form is `"x"/"a" + "y"/"b" + "z"/"c" = 1`, where a, b, c are the intercepts cut off by the plane at x, y, and z axes respectively.
Therefore, for the given equation, the intercept made with the x-axis is `5/2`.
APPEARS IN
संबंधित प्रश्न
Write the sum of intercepts cut off by the plane `vecr.(2hati+hatj-k)-5=0` on the three axes
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`
Write the equation of the plane whose intercepts on the coordinate axes are 2, −3 and 4.
A plane meets the coordinate axes at A, B and C, respectively, such that the centroid of triangle ABC is (1, −2, 3). Find the equation of the plane.
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 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 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.
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 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 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:
The intercepts made on the coordinate axes by the plane 2x + y − 2z = 3 are:
