The equation of a plane containing the point | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given plane is $2x + 3y - 4z = 17$. The normal vector to this plane is $\overline{n} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$.Since the required p

Vedclass · Accepted Answer

$\overline{r} \cdot (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) = -5$

Vedclass · Answer

(C) The given plane is $2x + 3y - 4z = 17$. The normal vector to this plane is $\overline{n} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$.Since the required plane is parallel to the given plane,it will have the same normal vector $\overline{n} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$.The equation of a plane passing through point $\overline{a} = \hat{i} - \hat{j} + \hat{k}$ and having normal $\overline{n}$ is given by $\overline{r} \cdot \overline{n} = \overline{a} \cdot \overline{n}$.Calculating $\overline{a} \cdot \overline{n} = (1)(2) + (-1)(3) + (1)(-4) = 2 - 3 - 4 = -5$.Thus,the equation of the plane is $\overline{r} \cdot (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) = -5$.

The equation of a plane containing the point $(1, -1, 1)$ and parallel to the plane $2x + 3y - 4z = 17$ is

Similar Questions

$A$ variable plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$,which is at a unit distance from the origin,cuts the coordinate axes at $A, B$,and $C$. If the centroid $(x, y, z)$ of $\triangle ABC$ satisfies $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=k$,then $k$ equals:

Find the vector equation of a plane which is at a distance of $7$ units from the origin and normal to the vector $3 \hat{i} + 5 \hat{j} - 6 \hat{k}$.

Find the distance of the point $(0, 0, 0)$ from the plane $3x - 4y + 12z = 3$. (in $/13$)

The angle between the planes $\vec{r} \cdot(2 \hat{i}+4 \hat{j}-3 \hat{k})=5$ and $\vec{r} \cdot(5 \hat{i}+3 \hat{j}+4 \hat{k})=7$ is

If $-2, \frac{4}{3}, \frac{-4}{5}$ are the intercepts made by a plane on $X, Y, Z$-axes respectively,then the direction cosines of a normal to this plane are

Vedclass Test Series

Exam Paper Generator

Online Exam Module