Let A be a point on the line vec{r} = (1 - 3m | vedclass

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

Question

(A) The coordinates of point $A$ on the line are $(1 - 3\mu, \mu - 1, 2 + 5\mu)$.The vector $\overrightarrow{AB}$ is given by $B - A = (3 - (1 - 3\mu)

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(A) The coordinates of point $A$ on the line are $(1 - 3\mu, \mu - 1, 2 + 5\mu)$.The vector $\overrightarrow{AB}$ is given by $B - A = (3 - (1 - 3\mu))\hat{i} + (2 - (\mu - 1))\hat{j} + (6 - (2 + 5\mu))\hat{k}$.$\overrightarrow{AB} = (2 + 3\mu)\hat{i} + (3 - \mu)\hat{j} + (4 - 5\mu)\hat{k}$.The vector $\overrightarrow{AB}$ is parallel to the plane $x - 4y + 3z = 1$ if and only if the dot product of $\overrightarrow{AB}$ and the normal vector of the plane $\vec{n} = (1, -4, 3)$ is zero.$(2 + 3\mu)(1) + (3 - \mu)(-4) + (4 - 5\mu)(3) = 0$.$2 + 3\mu - 12 + 4\mu + 12 - 15\mu = 0$.$(3 + 4 - 15)\mu + (2 - 12 + 12) = 0$.$-8\mu + 2 = 0$.$8\mu = 2 \Rightarrow \mu = \frac{2}{8} = \frac{1}{4}$.

Let $A$ be a point on the line $\vec{r} = (1 - 3\mu)\hat{i} + (\mu - 1)\hat{j} + (2 + 5\mu)\hat{k}$ and $B(3, 2, 6)$ be a point in space. Then the value of $\mu$ for which the vector $\overrightarrow{AB}$ is parallel to the plane $x - 4y + 3z = 1$ is

Similar Questions

The line $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ is parallel to which of the following planes?

The angle between the line $\bar{r}=(\hat{i}+2\hat{j}-\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$ and the plane $\bar{r} \cdot (2\hat{i}-\hat{j}+\hat{k})=4$ is:

The coordinates of the point where the line joining the points $(2, -3, 1)$ and $(3, -4, -5)$ intersects the plane $2x + y + z = 7$ are:

$A$ line drawn from the point $A(1, 3, 2)$ parallel to the line $\frac{x}{2} = \frac{y}{4} = \frac{z}{1}$ intersects the plane $3x + y + 2z = 5$ at point $B$. Then the coordinates of point $B$ are:

Find the equation of the plane passing through the intersection of the planes $x + 2y + 3z - 4 = 0$ and $2x + y - z + 5 = 0$ and perpendicular to the plane $5x + 3y + 6z + 8 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module