Question

Find the distance from the point \( A(2, 3, -1) \) to the given straight lines \( 2x - 2y + z + 3 = 0 \) and \( 3x - 2y + 2z + 17 = 0 \).

• A. \( \frac{1}{\sqrt{5}} \)
• B. 19.13
• C. \( \frac{3}{\sqrt{5}} \)
• D. \( \frac{6}{\sqrt{5}} \)

Hint:

The distance from a point \( (x_1, y_1, z_1) \) to a plane \( ax + by + cz + d = 0 \) is given by: \[ {Distance} = \frac{|ax_1 + by_1 + cz_1 + d|}{\sqrt{a^2 + b^2 + c^2}} \]

Answer 1

The Correct Option is D

Using the distance formula from a point to a plane, we calculate the distance from the point \( A(2, 3, -1) \) to the two planes. The distance to the first plane is \( \frac{6}{\sqrt{5}} \) units.