Question

Choose the most appropriate option. 
Find the distance from the point A (2, 3, -1) to the given straight line. $$x = 3t + 5, \quad y = 2t, \quad z = -2t - 25$$

• A. 15
• B. 17
• C. 19
• D. 21

Hint:

Use the formula for the distance between a point and a line in 3D to calculate the shortest distance.

Answer 1

The Correct Option is C

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: $$\text{Distance} = \boxed{19}$$