Question

Find the ratio in which ZX-plane divides the lines joining A(-2,3,4) and B(1.2.3)
​

Answer 1

Answer:

Ratio = -3 : 2

Step-by-step explanation:

Given:

• Point A (-2, 3, 4)
• Point B (1, 2, 3)

To Find:

• Ratio in which the line segment is divided by the ZX plane

Solution:

Let the line segment be divided in the ratio k : 1

Let the point of division be P = (x, y, z)

Here by given the line segment is divided by the ZX plane. Hence the y coordinate of the point of division is 0.

By section formula,

$\tt (x,y,z)=\bigg(\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ,\dfrac{m_1y_2+m_2y_1}{m_1+m_2} ,\dfrac{m_1z_2+m_2z_1}{m_1+m_2} \bigg)$

where y = 0, x₁ = -2, x₂ = 1, y₁ = 3, y₂ = 2, z₁ = 4, z₂ = 3, m₁ = k, m₂ = 1

Substitute the data,

$\tt (x.0,z) = \bigg(\dfrac{k-2}{k+1} ,\: \dfrac{2k+3}{k+1} ,\: \dfrac{3k+4}{k+1}\bigg)$

Equating the y coordinate,

$\tt \dfrac{2k+3}{k+1} =0$

2k + 3 = 0

2k = -3

k = -3/2

Hence the ratio of division of the line segment is -3 : 2

Here negative sign indicates that the line segment is divided externally.

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

Find the ratio in which ZX-plane divides the lines joining A(-2,3,4) and B(1,2,3)

$\huge{\boxed{\rm{\red{Answer}}}}$

$\large{\boxed{\sf{Let's \: understand \: the \: concept \: 1^{st}}}}$

$\large{\boxed{\sf{Given \: that}}}$

• A(-2,3,4)
• B(1,2,3)

$\large{\boxed{\sf{To \: find}}}$

• Ratio in which ZX - plane divides the line.

$\large{\boxed{\sf{Solution}}}$

• Ratio in which ZX - plane divides the line = -3 : 2

$\large{\boxed{\sf{Full \: solution}}}$

• Let the line segment be divided in ratio $\implies$ k:1
• Let the point of division be $\implies$ P = ( x,y,z )

$\large\purple{\texttt{According to the question}}$ ZX-plane divides the lines. $\large\purple{\texttt{Hence,}}$ the $\large\pink{\texttt{y}}$ coordinate of the point of the division is $\large\pink{\texttt{0.}}$

$\large\underbrace\mathfrak\green{By \: section's \: formula}$

• Formula is in attachment (1).
• Formula's value is in attachment (2)
• Substituting the value is in attachment (3)
• Equating the cordinate y is in attachment (4)

{ Do all things that is in above attachment } { Do formula or the other things also that is in attachment }

$\large\purple{\texttt{Hence,}}$

We have to asked to get the results in ratio so we have to convert fraction in ratio.

So, -3/2 is equal to -3:2

$\large{\boxed{\sf{-3:2 \: is \: the \: answer}}}$

@Itzbeautyqueen23

Hope it's helpful

Thank you :)