1. Explain the meaning of direction angles and their relation to direction vectors.
a. What are the direction angles of the vector [2, 4, -3]?
b. If a point P lies on the x-axis, what are the direction angles of the position vector OP ?
c. Prove that cos^2 (a )+ cos^2 (b )+ cos^2 (c ) = 1 (a,b,c are direction angles)
d. A vector has direction angles α = 75° and β= 55°
i. Find the value of γ
ii. Find a vector that has those direction angles
e. Explain why it is not possible for two of a vector's direction angles to be less than 45°
f. What is the value of sin^2 (a )+ sin^2 (b )+ sin^2 (c ) ? Why? (a,b,c are direction angles)