Vectors

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
2x+y-3z+1=0.

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