The angle made by the straight line x cosα + y sinα = p with the negative direction of x-axis is

(a) π/2+α
(b) α
(c) -α
(d) π/2-α.

Question

The angle made by the straight line x cosα + y sinα = p with the negative direction of x-axis is

(a) π/2+α
(b) α
(c) -α
(d) π/2-α.

Accepted Answer

>

> [!TLDR]
> The line $x\cos\alpha+y\sin\alpha=p$ is in normal form; its inclination to the positive $x$-axis is $\alpha+\pi/2$, so its angle with the negative $x$-axis is $\pi/2-\alpha$.
>
> In the normal form $x\cos\alpha+y\sin\alpha=p$, the vector $(\cos\alpha,\sin\alpha)$ is the unit normal to the line, making angle $\alpha$ with the positive $x$-axis. The line itself is perpendicular to this normal, so its direction vector is $(-\sin\alpha,\cos\alpha)$, which makes angle $\alpha+\pi/2$ with the positive $x$-axis.
> …

Q.The angle made by the straight line x cosα + y sinα = p with the negative direction of x-axis is

Concept understanding — Slope of a Line

Q.The angle made by the straight line x cosα + y sinα = p with the negative direction of x-axis is

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