The vector equation of the line whose Cartesi | vedclass

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

Question

(D) Given Cartesian equations are $y=2$ and $4x-3z+5=0$. From $4x-3z+5=0$,we have $4x = 3z-5$,which implies $4x = 3(z - \frac{5}{3})$. This can be wri

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given Cartesian equations are $y=2$ and $4x-3z+5=0$. From $4x-3z+5=0$,we have $4x = 3z-5$,which implies $4x = 3(z - \frac{5}{3})$. This can be written as $\frac{x}{3} = \frac{z - 5/3}{4}$. Since $y=2$,we can write the equation as $\frac{x-0}{3} = \frac{y-2}{0} = \frac{z-5/3}{4}$. This line passes through the point $(0, 2, 5/3)$ and has direction ratios $(3, 0, 4)$. The vector equation of a line passing through point $\vec{a}$ and parallel to vector $\vec{b}$ is $\vec{r} = \vec{a} + \lambda \vec{b}$. Here,$\vec{a} = 0\hat{i} + 2\hat{j} + \frac{5}{3}\hat{k}$ and $\vec{b} = 3\hat{i} + 0\hat{j} + 4\hat{k}$. Thus,the vector equation is $\vec{r} = (2\hat{j} + \frac{5}{3}\hat{k}) + \lambda(3\hat{i} + 4\hat{k})$.

The vector equation of the line whose Cartesian equations are $y=2$ and $4x-3z+5=0$ is

Similar Questions

The distance between the parallel lines $\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$ and $\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$ is

Let the shortest distance between the lines $\frac{x-3}{3}=\frac{y-\alpha}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-\beta}{4}$ be $3 \sqrt{30}$. Then the positive value of $5 \alpha+\beta$ is

If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$,then $\alpha + \beta + \gamma$ is equal to

If the mirror image of the point $P(3, 4, 9)$ in the line $\frac{x-1}{3} = \frac{y+1}{2} = \frac{z-2}{1}$ is $(\alpha, \beta, \gamma)$,then $14(\alpha+\beta+\gamma)$ is :

If the line passes through the points $P(6, -1, 2)$,$Q(8, -7, 2\lambda)$,and $R(5, 2, 4)$,then the value of $\lambda$ is $.......$

Vedclass Test Series

Exam Paper Generator

Online Exam Module