JEE ADVANCED: VECTORS AND 3D GEOMETRY ANALYSIS QUESTIONS AND ANSWERS

JEE ADVANCED: VECTORS AND 3D GEOMETRY ANALYSIS QUESTIONS AND ANSWERS 1. What is the centroid of triangle PQR when O is the origin?: Point S is the centroid of triangle PQR. 2. What is the equation of the plane that passes through (1,1,1) and is perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7?: 14x + 2y - 15z = 1. 3. If the point (α, β, 2) lies on the plane 3x + 3y - z + l = 0, what is the value of l?: The value of l is to be determined based on the given vectors. 4. What is the minimum value of cos(P+Q) + cos(Q+R) + cos(R+P) for triangle PQR?: The minimum value is to be determined based on the unit vectors in the directions of the sides of triangle PQR. 5. What is the relationship between sin(P + Q), sin(P + R), sin(Q + R), and sin 2R in triangle PQR?: