Question

A straight line drawn from the point P(1,3, 2), parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE ?

• A. The length of the line segment PQ is $\sqrt6$
• B. The coordinates of R are (1, 6, 3)
• C. The centroid of the triangle PQR is $(\frac{4}{3},\frac{14}{3},\frac{5}{3})$
• D. The perimeter of the triangle PQR is $\sqrt2+\sqrt6+\sqrt{11}$

Answer 1

Answer: (A), (C)

The length of the line segment PQ is $\sqrt6$

Answer 2

The correct option is (A): The length of the line segment PQ is $\sqrt6$ and (C): The centroid of the triangle PQR is $(\frac{4}{3},\frac{14}{3},\frac{5}{3})$.