1. In Δ ABC, with usual notations, prove that a=b(cosC)+c(cosB) using vectors.
2. Prove by vector method that in ΔABC, b²=c²+a²-2ac(cosB).
3. Find the angle between the two diagonals of a cube by vector method.
4. Find the equation of the plane through (1,2,3) and parallel to
5. Derive the formula to get the angle between two planes.
6. Prove that the points (1,2,3), (3,-1,2), (-2,3,1), and (6,-4,2) are coplanar.
7. Prove suing vectors that
sin(A+B) = sinAcosB+cosAsinB
8. Find the angle between the planes 2x+y-z=9 and x+2y+z=7.
9. Using vectors show that
10. Find the vector and Cartesian equation of a plane through the points (1,2,3), (1,0,-1), and (2,1,2).