# Find The Equation Of The Line In Vector And In Cartesian Form That Passes Through The Point With Position Vector 2i^− J^+4 K^ And Is In The Direction I^+2 J^− K^.

Given:

The line passes through the point with position vector:

$\vec{a} = 2\hat{i} – \hat{j} + 4\hat{k}$—[1] $\vec{b} = \hat{i} + 2 \hat{j} – \hat{k}$—[2]

As we know, a line through a point with position vector $\vec{a}$and parallel to

$\vec{b}$ is given by the equation:

$\vec{r} = \vec{a} + \lambda\vec{b}$ $\Rightarrow \vec{r} = 2\hat{i} – \hat{j} + 4\hat{k} + \lambda (\hat{i} + 2\hat{j} – \hat{k})$

This is the required equation of the line in vector form.

$\Rightarrow x\hat{i} – y \hat{j} + z\hat{k} + (\lambda + 2) \hat{i} + (2\lambda – 1)\hat{j} + (-\lambda + 4)\hat{k}$

Now by eliminating λ, we get the Cartesian form equation:

$\frac{x-2}{1} = \frac{y+1}{2} = \frac{z-4}{1}$

Explore more such questions and answers at BYJU’S.

Was this answer helpful?

0 (0)

(0)
(0)

#### Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.