Consider the following for the next two (02) items that follow :

Let a vector $\vec{a}=4 \hat{i}-8 \hat{j}+\hat{k}$ make angles α, β, γ with the positive directions of x, y, z axes respectively. 

Consider the following for the next two (02) items that follow :

The position vectors of two points A and B are î - ĵ and ĵ + k̂ respectively. 

Consider the following points :

1. (-1, -3, 1)

2. (-1, 3, 2)

3. (-2, 5, 3)

Which of the above points lie on the line joining A and B ?  

Consider the following for the next two (02) items that follow :

The position vectors of two points A and B are î - ĵ and ĵ + k̂ respectively. 

Consider the following for the next three (03) items that follow :

Let f(x) = Pe^x + Qe^2x + Re^3x where P, Q, R are real numbers. Further f(0) = 6, f'(ln 3) = 282 and $\int_0^{\ln 2} f(x) d x=11$