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What is the locus of a point (x , y , z)...

What is the locus of a point `(x , y , z)` for which `y=0, z=0?`

A

equation of X - axis

B

equation of y-axis

C

equation at Z-axis

D

none of these

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The correct Answer is:
To find the locus of a point \((x, y, z)\) for which \(y = 0\) and \(z = 0\), we can follow these steps: ### Step 1: Understand the conditions We are given two conditions: 1. \(y = 0\) 2. \(z = 0\) ### Step 2: Analyze the implications The condition \(y = 0\) means that the point lies in the plane where the y-coordinate is zero. This is the x-z plane. The condition \(z = 0\) means that the point lies in the plane where the z-coordinate is zero. This is the x-y plane. ### Step 3: Combine the conditions When both conditions \(y = 0\) and \(z = 0\) are satisfied simultaneously, we are left with: - \(y = 0\) (the x-z plane) - \(z = 0\) (the x-y plane) ### Step 4: Determine the locus The only coordinate that can vary is \(x\). Therefore, the locus of the point \((x, y, z)\) under the given conditions is: - All points where \(y = 0\) and \(z = 0\) can be represented as \((x, 0, 0)\). This means the locus is the x-axis. ### Conclusion Thus, the locus of the point \((x, y, z)\) for which \(y = 0\) and \(z = 0\) is the equation of the x-axis.
To find the locus of a point \((x, y, z)\) for which \(y = 0\) and \(z = 0\), we can follow these steps: ### Step 1: Understand the conditions We are given two conditions: 1. \(y = 0\) 2. \(z = 0\) ### Step 2: Analyze the implications ...
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