The Cartesian equation of the line which pass | vedclass

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Question

(B) The Cartesian equation of a line passing through a point $(x_1, y_1, z_1)$ and parallel to a vector $a \hat{i} + b \hat{j} + c \hat{k}$ is given b

Vedclass · Accepted Answer

$\frac{x-5}{3} = \frac{y+2}{2} = \frac{z-4}{-8}$

Vedclass · Answer

(B) The Cartesian equation of a line passing through a point $(x_1, y_1, z_1)$ and parallel to a vector $a \hat{i} + b \hat{j} + c \hat{k}$ is given by the formula: $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$ Here,the point is $(x_1, y_1, z_1) = (5, -2, 4)$ and the direction vector is $3 \hat{i} + 2 \hat{j} - 8 \hat{k}$,so $(a, b, c) = (3, 2, -8)$. Substituting these values into the formula,we get: $\frac{x - 5}{3} = \frac{y - (-2)}{2} = \frac{z - 4}{-8}$ Simplifying this,we obtain: $\frac{x - 5}{3} = \frac{y + 2}{2} = \frac{z - 4}{-8}$ Thus,option $B$ is the correct answer.

The Cartesian equation of the line which passes through the point $(5, -2, 4)$ and is parallel to the vector $3 \hat{i} + 2 \hat{j} - 8 \hat{k}$ is:

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