The Cartesian equation of a line is 3x + 1 = | vedclass

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

Question

(D) Given the Cartesian equation: $3x + 1 = 6y - 2 = -z + 1$. First,rewrite the equation in the standard form $\frac{x - x_1}{a} = \frac{y - y_1}{b} =

Vedclass · Accepted Answer

$\overline{r} = (-\frac{1}{3} \hat{i} + \frac{1}{3} \hat{j} + \hat{k}) + \lambda(2 \hat{i} + \hat{j} - 6 \hat{k})$

Vedclass · Answer

(D) Given the Cartesian equation: $3x + 1 = 6y - 2 = -z + 1$. First,rewrite the equation in the standard form $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$. $3(x + \frac{1}{3}) = 6(y - \frac{1}{3}) = -(z - 1)$. Dividing by the least common multiple of the coefficients $(6)$,we get: $\frac{x + 1/3}{1/3} = \frac{y - 1/3}{1/6} = \frac{z - 1}{-1}$. To simplify the direction ratios,multiply the denominators by $6$: $\frac{x + 1/3}{2} = \frac{y - 1/3}{1} = \frac{z - 1}{-6}$. The point on the line is $(-\frac{1}{3}, \frac{1}{3}, 1)$ and the direction vector is $2 \hat{i} + \hat{j} - 6 \hat{k}$. Thus,the vector equation is $\overline{r} = (-\frac{1}{3} \hat{i} + \frac{1}{3} \hat{j} + \hat{k}) + \lambda(2 \hat{i} + \hat{j} - 6 \hat{k})$.

The Cartesian equation of a line is $3x + 1 = 6y - 2 = -z + 1$. Find its vector equation.

Similar Questions

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

If $P$ is a point lying on the line passing through the point $A(\hat{i}-\hat{j}+3 \hat{k})$ and parallel to the vector $2 \hat{i}+\hat{j}-2 \hat{k}$ such that $|AP|=18$,then a position vector of $P$ is

If the shortest distance between the lines $\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}$ and $\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$,then the sum of all possible values of $\lambda$ is :

The direction ratios of a bisector of the angle between two lines whose direction ratios are $1, 1, 2$ and $\sqrt{3}, -\sqrt{3}, 0$ are

The equation of the line passing through the points $(3, 4, -7)$ and $(6, -1, 1)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module