Find the Cartesian equation of the line passi | vedclass

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Question

(A) Let the given points be $A(2, -1, 1)$ and $B(-1, 4, 1)$. The direction vector $\vec{v}$ of the line joining $A$ and $B$ is given by $\vec{v} = \ve

Vedclass · Accepted Answer

$\frac{x - 1}{-3} = \frac{y - 2}{5} = \frac{z - 2}{0}$

Vedclass · Answer

(A) Let the given points be $A(2, -1, 1)$ and $B(-1, 4, 1)$. The direction vector $\vec{v}$ of the line joining $A$ and $B$ is given by $\vec{v} = \vec{B} - \vec{A} = (-1 - 2)\hat{i} + (4 - (-1))\hat{j} + (1 - 1)\hat{k} = -3\hat{i} + 5\hat{j} + 0\hat{k}$.Since the required line is parallel to this line,its direction ratios are proportional to $(-3, 5, 0)$.The line passes through the point $P(1, 2, 2)$.The Cartesian equation of a line passing through $(x_1, y_1, z_1)$ with direction ratios $(a, b, c)$ is $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$.Substituting the values,we get $\frac{x - 1}{-3} = \frac{y - 2}{5} = \frac{z - 2}{0}$.

Find the Cartesian equation of the line passing through the point $\hat{i} + 2\hat{j} + 2\hat{k}$ and parallel to the line joining the points $2\hat{i} - \hat{j} + \hat{k}$ and $-\hat{i} + 4\hat{j} + \hat{k}$.

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