The Cartesian equation of a line is frac{x+2} | vedclass

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

Question

(A) The Cartesian equation of a line is given by $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$.Comparing this with the given equation $\frac{x-(-2

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The Cartesian equation of a line is given by $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$.Comparing this with the given equation $\frac{x-(-2)}{3}=\frac{y-4}{2}=\frac{z-5}{5}$,we identify the point $(x_1, y_1, z_1) = (-2, 4, 5)$ through which the line passes.The direction ratios $(a, b, c)$ are $(3, 2, 5)$.The vector equation of a line passing through a point with position vector $\vec{a}$ and parallel to a vector $\vec{b}$ is given by $\vec{r} = \vec{a} + \lambda \vec{b}$.Here,$\vec{a} = -2 \hat{i} + 4 \hat{j} + 5 \hat{k}$ and $\vec{b} = 3 \hat{i} + 2 \hat{j} + 5 \hat{k}$.Thus,the vector equation is $\vec{r} = (-2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + \lambda(3 \hat{i} + 2 \hat{j} + 5 \hat{k})$.

The Cartesian equation of a line is $\frac{x+2}{3}=\frac{y-4}{2}=\frac{z-5}{5}$,then the vector equation of the line is

Similar Questions

Let in a $\triangle ABC$,the length of the side $AC$ be $6$,the vertex $B$ be $(1,2,3)$ and the vertices $A, C$ lie on the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Then the area (in sq. units) of $\triangle ABC$ is

The distance between parallel lines $\vec{r}=(2\hat{i}-\hat{j}+\hat{k})+\lambda(2\hat{i}+\hat{j}-2\hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu(2\hat{i}+\hat{j}-2\hat{k})$ is

The angle between the lines $\bar{r}=(3 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})$ and $\bar{r}=(5 \hat{i}-2 \hat{k})+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})$ is:

If the line passing through $(5, 1, a)$ and $(3, b, 1)$ intersects the $yz$-plane at $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$,then find the values of $a$ and $b$.

Find the coordinates of the point where the line passing through $(5, 1, 6)$ and $(3, 4, 1)$ crosses the $ZX$-plane.

Vedclass Test Series

Exam Paper Generator

Online Exam Module