The equation of the plane passing through 3 h | vedclass

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

Question

(B) The plane passes through the point $\vec{a} = 3 \hat{i} + 2 \hat{j} + 6 \hat{k}$ and is parallel to the vectors $\vec{b} = 2 \hat{i} + \hat{j} + \

Vedclass · Accepted Answer

$2 x-y-3 z=-14$

Vedclass · Answer

(B) The plane passes through the point $\vec{a} = 3 \hat{i} + 2 \hat{j} + 6 \hat{k}$ and is parallel to the vectors $\vec{b} = 2 \hat{i} + \hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + \hat{k}$.The normal vector $\vec{N}$ to the plane is given by the cross product of the two parallel vectors:$\vec{N} = \vec{b} 	imes \vec{c} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 1 & 1 \ 1 & -1 & 1 \end{vmatrix}$$\vec{N} = \hat{i}(1 - (-1)) - \hat{j}(2 - 1) + \hat{k}(-2 - 1) = 2 \hat{i} - \hat{j} - 3 \hat{k}$.The equation of the plane is $(\vec{r} - \vec{a}) \cdot \vec{N} = 0$,where $\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$.$((x-3) \hat{i} + (y-2) \hat{j} + (z-6) \hat{k}) \cdot (2 \hat{i} - \hat{j} - 3 \hat{k}) = 0$$2(x-3) - 1(y-2) - 3(z-6) = 0$$2x - 6 - y + 2 - 3z + 18 = 0$$2x - y - 3z + 14 = 0$$2x - y - 3z = -14$.

The equation of the plane passing through $3 \hat{i}+2 \hat{j}+6 \hat{k}$ and parallel to the vectors $2 \hat{i}+\hat{j}+\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is

Similar Questions

The equation of the plane passing through the point $(2, -1, -3)$ and parallel to the lines $\frac{x-1}{3} = \frac{y+2}{2} = \frac{z}{-4}$ and $\frac{x}{2} = \frac{y-1}{-3} = \frac{z-2}{2}$ is

In space,the equation $by + cz + d = 0$ represents a plane perpendicular to the

Find the equation of the plane passing through the point $(-1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$.

The angle between the planes $x+y+2z=6$ and $2x-y+z=9$ is:

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of $\triangle ABC$ is at the point $(1, 2, 3)$,then the equation of the plane is

Vedclass Test Series

Exam Paper Generator

Online Exam Module