Question:
The plane XOZ divides the line joining of (1,-1,5) and (2,3,4) in the ratio $\lambda : 1$ then the value of $\lambda = $
The plane XOZ divides the line joining of (1,-1,5) and (2,3,4) in the ratio $\lambda : 1$ then the value of $\lambda = $
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A coordinate plane (like $y=0$) divides a line in the ratio of the coordinates of the missing variable ($-y_1/y_2$).
Updated On: Jul 3, 2026
- 3
- -3
- $\frac{1}{3}$
- $-\frac{1}{3}$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
The XOZ plane is the plane $y = 0$. The ratio in which a plane $y = 0$ divides the segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is $-y_1 : y_2$.
Step 2: Meaning
Here $y_1 = -1$ and $y_2 = 3$.
Step 3: Analysis
Ratio $\lambda : 1 = -(-1) : 3 = 1 : 3$.
Step 4: Conclusion
Thus, $\lambda = 1/3$. Final Answer: (C)
The XOZ plane is the plane $y = 0$. The ratio in which a plane $y = 0$ divides the segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is $-y_1 : y_2$.
Step 2: Meaning
Here $y_1 = -1$ and $y_2 = 3$.
Step 3: Analysis
Ratio $\lambda : 1 = -(-1) : 3 = 1 : 3$.
Step 4: Conclusion
Thus, $\lambda = 1/3$. Final Answer: (C)
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