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Plane x + y +z = 1 cuts the x, y, z. Axi...

Plane `x + y +z = 1` cuts the x, y, z. Axis at A, B, C respectively the distance of plane from point P such that OP = PA = PB = PC is D, then `4sqrt(3)D` = (where O is origin)

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To solve the problem step by step, we will follow the reasoning presented in the video transcript. ### Step 1: Identify the points where the plane intersects the axes The plane given is \(x + y + z = 1\). To find where this plane intersects the x, y, and z axes, we set the other two variables to zero: - For the x-axis (where \(y = 0\) and \(z = 0\)): \[ x + 0 + 0 = 1 \implies x = 1 \implies A(1, 0, 0) \] - For the y-axis (where \(x = 0\) and \(z = 0\)): \[ 0 + y + 0 = 1 \implies y = 1 \implies B(0, 1, 0) \] - For the z-axis (where \(x = 0\) and \(y = 0\)): \[ 0 + 0 + z = 1 \implies z = 1 \implies C(0, 0, 1) \]
To solve the problem step by step, we will follow the reasoning presented in the video transcript. ### Step 1: Identify the points where the plane intersects the axes The plane given is \(x + y + z = 1\). To find where this plane intersects the x, y, and z axes, we set the other two variables to zero: - For the x-axis (where \(y = 0\) and \(z = 0\)): \[ x + 0 + 0 = 1 \implies x = 1 \implies A(1, 0, 0) ...
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