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प्रश्न
Find the length of the perpendicular from the point (1, – 2, 3) to the plane x – y + z = 5
उत्तर
Perpendicular length from the point (x1, y1, z1) to the plane ax + by + cz + d = 0 is `|("a"x_1 + "b"y_1 + "c"z_1 + "d")/sqrt("a"^2 + "b"^2 + "c"^2)|`
Given point (1, – 2, 3) and the plane x – y + z = 5
∴ Length of the perpendicular = `|(1 - (- 2) + 3 - 5)/sqrt((1)^2 + (- 1)^2 + (1)^2)|`
= `|(1 + 2 + 3 - 5)/sqrt(3)|`
= `1/sqrt(3)` units
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