Find the ratio in which ZX-plane divides the lines joining A(-2,3,4) and B(1.2.3)
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Find the ratio in which ZX-plane divides the lines joining A(-2,3,4) and B(1.2.3)
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Answer:
Ratio = -3 : 2
Step-by-step explanation:
Given:
To Find:
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,
[tex]\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)[/tex]
where y = 0, x₁ = -2, x₂ = 1, y₁ = 3, y₂ = 2, z₁ = 4, z₂ = 3, m₁ = k, m₂ = 1
Substitute the data,
[tex]\tt (x.0,z) = \bigg(\dfrac{k-2}{k+1} ,\: \dfrac{2k+3}{k+1} ,\: \dfrac{3k+4}{k+1}\bigg)[/tex]
Equating the y coordinate,
[tex]\tt \dfrac{2k+3}{k+1} =0[/tex]
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.
Verified answer
[tex]\huge{\boxed{\rm{\red{Question}}}}[/tex]
Find the ratio in which ZX-plane divides the lines joining A(-2,3,4) and B(1,2,3)
[tex]\huge{\boxed{\rm{\red{Answer}}}}[/tex]
[tex]\large{\boxed{\sf{Let's \: understand \: the \: concept \: 1^{st}}}}[/tex]
[tex]\large{\boxed{\sf{Given \: that}}}[/tex]
[tex]\large{\boxed{\sf{To \: find}}}[/tex]
[tex]\large{\boxed{\sf{Solution}}}[/tex]
[tex]\large{\boxed{\sf{Full \: solution}}}[/tex]
[tex]\large\purple{\texttt{According to the question}}[/tex] ZX-plane divides the lines. [tex]\large\purple{\texttt{Hence,}}[/tex] the [tex]\large\pink{\texttt{y}}[/tex] coordinate of the point of the division is [tex]\large\pink{\texttt{0.}}[/tex]
[tex]\large\underbrace\mathfrak\green{By \: section's \: formula}[/tex]
{ Do all things that is in above attachment } { Do formula or the other things also that is in attachment }
[tex]\large\purple{\texttt{Hence,}}[/tex]
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
[tex]\large{\boxed{\sf{-3:2 \: is \: the \: answer}}}[/tex]
@Itzbeautyqueen23
Hope it's helpful
Thank you :)