The equation of the line passing through (1, | vedclass

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

Question

(A) Let the direction ratios of the line be $(l, m, n)$.Since the line is parallel to the planes $x - y + 2z = 5$ and $3x + y + z = 6$,it must be perp

Vedclass · Accepted Answer

$\frac{x - 1}{-3} = \frac{y - 2}{5} = \frac{z - 3}{4}$

Vedclass · Answer

(A) Let the direction ratios of the line be $(l, m, n)$.Since the line is parallel to the planes $x - y + 2z = 5$ and $3x + y + z = 6$,it must be perpendicular to the normals of these planes.The normals are $\vec{n_1} = (1, -1, 2)$ and $\vec{n_2} = (3, 1, 1)$.Thus,$l - m + 2n = 0$ and $3l + m + n = 0$.Using the cross product to find the direction ratios $(l, m, n) = \vec{n_1} 	imes \vec{n_2}$:$l = (-1)(1) - (2)(1) = -3$$m = (2)(3) - (1)(1) = 5$$n = (1)(1) - (-1)(3) = 4$So,the direction ratios are $(-3, 5, 4)$.The line passes through $(1, 2, 3)$,so its equation is $\frac{x - 1}{-3} = \frac{y - 2}{5} = \frac{z - 3}{4}$.

The equation of the line passing through $(1, 2, 3)$ and parallel to the planes $x - y + 2z = 5$ and $3x + y + z = 6$ is:

Similar Questions

The equation of the plane passing through the line of intersection of the planes $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1$ and $\vec{r} \cdot(2 \hat{i}+3 \hat{j}-\hat{k})+4=0$ and parallel to the $x$-axis is:

The plane $lx + my = 0$ is rotated by an angle $\alpha$ about its line of intersection with the plane $z = 0$. Find the equation of the plane in its new position.

The equation of the plane containing the line $2x - 5y + z = 3; x + y + 4z = 5$ and parallel to the plane $x + 3y + 6z = 1$ is:

The vector equation of the plane passing through the intersection of the planes $\overrightarrow{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1$ and $\overrightarrow{r} \cdot (\hat{i} - 2\hat{j}) = -2$,and the point $(1, 0, 2)$ is:

If the line $\frac{x+1}{1}=\frac{y-k}{11}=\frac{z-4}{-5}$ lies in the plane $2x+py+7z-41=0$ which is perpendicular to the plane $x+4y-2z+13=0$,then $k=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module