Question
Download Solution PDFDetermine the co-ordinates of the point where the line through the points A (2, 3, 2) and B (5, 1, 6) crosses the XY- plane?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A(2, 3, 2) and B(5, 1, 6) are two points.
Concept:
The cartesian equation of a line passing through A(x1, y1, z1) and B(x2, y2, z2) is given by,
Calculation:
Here, x1 = 2, y1 = 3, z1 = 2, x2 = 5, y2 = 1 and z2 = 6
The cartesian equation of a required line is:
⇒
⇒
The line crosses xy - plane , i.e., z = 0
So, by substituting z = 0 in equation (1), we get
⇒
⇒
⇒
⇒ 2x - 4 = - 3 and 2y - 6 = 2
⇒ 2x = 1 and 2y = 8
⇒ x =
∴ The line AB crosses the XY-plane at (1/2, 4. 0)
Last updated on Jul 7, 2025
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