The vector equation of the line frac{x+3}{2}= | vedclass

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

Question

(B) The given equation of the line is $\frac{x+3}{2}=\frac{2y-3}{5}; z=-1$. First,rewrite the equation in the standard form $\frac{x-x_1}{a}=\frac{y-y

Vedclass · Accepted Answer

$\bar{r}=\left(-3 \hat{i}+\frac{3}{2} \hat{j}-\hat{k}\right)+\lambda(4 \hat{i}+5 \hat{j})$

Vedclass · Answer

(B) The given equation of the line is $\frac{x+3}{2}=\frac{2y-3}{5}; z=-1$. First,rewrite the equation in the standard form $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$. $\frac{x+3}{2}=\frac{2(y-3/2)}{5}; z=-1$ $\frac{x-(-3)}{2}=\frac{y-3/2}{5/2}; z=-1$. This line passes through the point $(-3, 3/2, -1)$ and has direction ratios proportional to $(2, 5/2, 0)$. Multiplying the direction ratios by $2$,we get $(4, 5, 0)$. 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,$\vec{a}=-3\hat{i}+\frac{3}{2}\hat{j}-\hat{k}$ and $\vec{b}=4\hat{i}+5\hat{j}$. Thus,the vector equation is $\vec{r}=\left(-3\hat{i}+\frac{3}{2}\hat{j}-\hat{k}\right)+\lambda(4\hat{i}+5\hat{j})$.

The vector equation of the line $\frac{x+3}{2}=\frac{2y-3}{5}; z=-1$ is

Similar Questions

Let $(\alpha, \beta, \gamma)$ be the image of the point $A(8, 5, 7)$ in the line $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}$. Then $\alpha + \beta + \gamma$ is equal to

Let the area of the triangle formed by the lines $x+2=y-1=z$,$\frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}$ and $\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}$ be $A$. Then $A^2$ is equal to . . . . . . .

$L_1$ is a line passing through the points with position vectors $\hat{i}-2 \hat{j}-\hat{k}$ and $4 \hat{i}-3 \hat{k}$. $L_2$ is a line passing through the points with position vectors $\hat{i}+2 \hat{j}-\hat{k}$ and $2 \hat{i}-4 \hat{j}-5 \hat{k}$. Then the distance between $L_1$ and $L_2$ is

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\lambda}{2}=\frac{z}{1}$ intersect each other,then $\lambda = \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module