Question

The vertices B and C of a triangle ABC lie on the line \( \frac{x}{1} = \frac{1-y}{2} = \frac{z-2}{3} \). The coordinates of A and B are (1, 6, 3) and (4, 9, 6) respectively and C is at a distance of 10 units from B. The area (in sq. units) of \( \triangle ABC \) is:

• A. \( 10\sqrt{13} \)
• B. \( 15\sqrt{13} \)
• C. \( 5\sqrt{13} \)
• D. \( 20\sqrt{13} \)

Hint:

Always rewrite the line equation in standard form \( \frac{x-x_1}{a} = \frac{y-y_1}{b} = \frac{z-z_1}{c} \) to correctly identify the direction vector.

Answer 1

The Correct Option is C