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Find the length of the intercept, cut off by the plane 2x + y − z = 5 on the x-axis - Mathematics

Sum
Find the length of the intercept, cut off by the plane 2x + y − z = 5 on the x-axis
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Solution

The given plane is  2x + y - x = 5
Dividing both sides of the equation by 5, we obtain

`2/5"x" + "y"/5 - "z"/5 = 1`

⇒ `"x"/(5/2) + "y"/5 + "z"/(-5) = 1`

It is known that the equation of a plane in intercept form is `"x"/"a" + "y"/"b" + "z"/"c" = 1`, where a, b, c are the intercepts cut off by the plane at x, y, and z axes respectively.

Therefore, for the given equation, the intercept made with the x-axis is `5/2`.

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