Write the vector equation of the following line:
$\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{6 - z}{2}$

Solution

$The given equation of line is \frac{x - 5}{3} = \frac{y + 4}{7} = \frac{6 - z}{2} i . e . in standard form \frac{x - 5}{3} = \frac{y - (- 4)}{7} = \frac{z - 6}{- 2} Comparing this equation with standard form \frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$

We get, x₁ = 5, y₁ = -4, z₁ = 6, a = 3, b = 7, c = -2

Thus, the required line is parallel to the vector $3 \hat{i} + 7 \hat{j} - 2 k$ and passes through the point ( 5, -4, 6 ).

The vector form of the line can be written as $\vec{r} = \vec{a} + λ \vec{b},$ where $λ$ is a constant.

Thus, the required equation is $\vec{r} = (5 \hat{i} - 4 \hat{j} + 6 k) + λ (3 \hat{i} + 7 \hat{j} - 2 k)$

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Three Dimensional Geometry

Write the vector equation of the following line:
$\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{6 - z}{2}$

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Find the direction cosines of x, y and z-axis.

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Three Dimensional Geometry

Write the vector equation of the following line:x - 53 = y + 47 = 6 - z2

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Write the vector equation of the following line:
$\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{6 - z}{2}$