Question:
Choose the most appropriate option.
Find the distance from the point A (2, 3, -1) to the given straight line. \[ x = 3t + 5, \quad y = 2t, \quad z = -2t - 25 \]
Choose the most appropriate option.
Find the distance from the point A (2, 3, -1) to the given straight line. \[ x = 3t + 5, \quad y = 2t, \quad z = -2t - 25 \]
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Use the formula for the distance between a point and a line in 3D to calculate the shortest distance.
Updated On: July 22, 2025
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The Correct Option is C
Solution and Explanation
The distance from a point \( A(x_1, y_1, z_1) \) to a line defined parametrically as \( x = x_0 + at, y = y_0 + bt, z = z_0 + ct \) is given by the formula:
\[
\text{Distance} = \frac{|(x_1 - x_0)(b) - (y_1 - y_0)(a) + (z_1 - z_0)(c)|}{\sqrt{a^2 + b^2 + c^2}}
\]
Substituting the values:
\[
\text{Distance} = \boxed{19}
\]
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