Question:
The co-ordinates of the point where the line joining the points \((3,5,-7)\) and \((-2,1,8)\) is intersected by the YOZ plane are
The co-ordinates of the point where the line joining the points \((3,5,-7)\) and \((-2,1,8)\) is intersected by the YOZ plane are
Show Hint
On the YOZ plane x = 0; write the line in parametric form and find the parameter.
Updated On: Oct 1, 2026
- \((0,\frac{-13}{5},\frac{2}{5})\)
- \((0,\frac{13}{5},\frac{2}{5})\)
- \((0,\frac{13}{5},2)\)
- \((0,\frac{-13}{5},-2)\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
The YOZ plane is \(x = 0\). Points on the line joining \((3, 5, -7)\) and \((-2, 1, 8)\) are \((3 - 5t,\ 5 - 4t,\ -7 + 15t)\).
Step 2: Solve for t
\(3 - 5t = 0\), so \(t = \frac35\).
Step 3: Find y and z
\[ y = 5 - \frac{12}{5} = \frac{13}{5},\qquad z = -7 + 9 = 2 \]
The point is \(\left(0, \frac{13}{5}, 2\right)\), option (C). Option (B) has \(z = 2/5\), which does not match.
Final Answer:
The point is \(\left(0, \frac{13}{5}, 2\right)\), option (C). \[ \boxed{\left(0,\frac{13}{5},2\right)} \]
The YOZ plane is \(x = 0\). Points on the line joining \((3, 5, -7)\) and \((-2, 1, 8)\) are \((3 - 5t,\ 5 - 4t,\ -7 + 15t)\).
Step 2: Solve for t
\(3 - 5t = 0\), so \(t = \frac35\).
Step 3: Find y and z
\[ y = 5 - \frac{12}{5} = \frac{13}{5},\qquad z = -7 + 9 = 2 \]
The point is \(\left(0, \frac{13}{5}, 2\right)\), option (C). Option (B) has \(z = 2/5\), which does not match.
Final Answer:
The point is \(\left(0, \frac{13}{5}, 2\right)\), option (C). \[ \boxed{\left(0,\frac{13}{5},2\right)} \]
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