Question

Find the equation of line parallel to x-axis and passing through the origin​

Answer 1

EXPLANATION.

Equation of the line parallel to x-axis passing through the origin.

Direction cosines the line making,

α with x-axis, β with y-axis, γ with z-axis are x, y, z.

x = Cosα, y = Cosβ, z = Cosγ.

⇒ x = Cos(0)°.

⇒ y = Cos(90°).

⇒ z = Cos(90°).

⇒ x = 1.

⇒ y = 0.

⇒ z = 0.

Direction Cosines of x-axis = (1,0,0).

                                                                                           

MORE INFORMATION.

Equation of line.

(1) = Vector form.

Equation of line passing through $\sf A( \vec {a})$ and parallel to vector $\sf \vec {b}$.

$\sf \implies \boxed {\vec {r} = \vec {a} + \lambda \vec {b}}$

(2) = Cartesian form.

Equation of a straight line passing through a fixed point (x₁, y₁, z₁) and having direction ratios a, b, c.

x - x₁/a = y - y₁/b = z - z₁/c.

Equation of a line passing through two given points.

(1) = Vector form.

Equation of line passing through two points  $\sf A (\vec {a})$ and $\sf B (\vec {b})$

$\sf \implies \boxed {\vec {r} = \vec {a} + \lambda ( \vec {b} - \vec {a} )}$

(2) = Cartesian form.

Equation of a line passing through two given points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by.

x - x₁/x₂ - x₁ = y - y₁/y₂ - y₁ = z - z₁/z₂ - z₁.

Answer 2

★$\huge\bf{\blue{\underline{Question:-}}}$

☯ $\large\bf{\green{Find\: the \:equation \:of\: line\: parallel}} \\ \large\bf{\green{ to\: x-axis\: and\: passing\: through}} \\ \large\bf{\green{the\: origin\:}}$

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★$\huge\bf{\red{\underline{Answer:-}}}$

• ☯ $\large\sf{\green{Direction\:cosines\:of\:x–axis\:(1,0,0).}}$

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★$\huge\bf{\pink{\underline{Explanation:-}}}$

☯ $\large\bf{\green{Direction\:cosines\:the\:line\:making.}}$

• ☯ $\large\sf{\alpha\:with\:x–axis}$
• ☯ $\large\sf{\beta\:with\:y–axis}$
• ☯ $\large\sf{\gamma\:with\:z–axis}$
• ➙$\large\sf{x,y,z.}$

★$\huge\bf{\purple{\underline{Then,:-}}}$

• ☯ $\large\sf{x=Cos\alpha}$
• ☯ $\large\sf{y=Cos\beta}$
• ☯ $\large\sf{z=Cos\gamma}$

★$\huge\bf{\orange{\underline{Then,:-}}}$

• ➙ $\large\sf{x=Cos(0°)}$
• ➙ $\large\sf{y=Cos(90°)}$
• ➙ $\large\sf{z=Cos(90°)}$
• ➙ $\large\sf{x=1}$
• ➙ $\large\sf{y=0}$
• ➙ $\large\sf{z=0}$

☯ $\large\sf{\green{Direction\:cosines\:of\:x–axis\:(1,0,0).}}$

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