Question:
The inclination of the line x - y + 3 = 0 with the positive direction of x-axis is
The inclination of the line x - y + 3 = 0 with the positive direction of x-axis is
Updated On: Jul 7, 2022
- $45^{\circ}$
- $135^{\circ}$
- $- 45^{\circ}$
- $- 135^{\circ}$
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The Correct Option is A
Solution and Explanation
The equation of the line x - y + 3 = 0 can be rewritten as y = x + 3
$\Rightarrow$ m = tan $\theta$ = 1 and hence $\theta = 45^{\circ}$.
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Concepts Used:
Equation of a Line in Space
In a plane, the equation of a line is given by the popular equation y = m x + C. Let's look at how the equation of a line is written in vector form and Cartesian form.
Vector Equation
Consider a line that passes through a given point, say ‘A’, and the line is parallel to a given vector '\(\vec{b}\)‘. Here, the line ’l' is given to pass through ‘A’, whose position vector is given by '\(\vec{a}\)‘. Now, consider another arbitrary point ’P' on the given line, where the position vector of 'P' is given by '\(\vec{r}\)'.
\(\vec{AP}\)=𝜆\(\vec{b}\)
Also, we can write vector AP in the following manner:
\(\vec{AP}\)=\(\vec{OP}\)–\(\vec{OA}\)
𝜆\(\vec{b}\) =\(\vec{r}\)–\(\vec{a}\)
\(\vec{a}\)=\(\vec{a}\)+𝜆\(\vec{b}\)
\(\vec{b}\)=𝑏1\(\hat{i}\)+𝑏2\(\hat{j}\) +𝑏3\(\hat{k}\)