If l,m,n and a,b,c are direction cosines of two lines then
they are parallel when la + mb + nc = 0
they are perpendicular when \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}\)
the direction ratios of the bisectors of the angles between l±a, m±b, n±c
the direction ratios of the bisectors of the angles between l±a, m±b, n±c
The correct option is: (C) the direction ratios of the bisectors of the angles between l±a, m±b, n±c
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \( f(x + y) = f(x) f(y) \) for all \( x, y \in \mathbb{R} \). If \( f'(0) = 4a \) and \( f \) satisfies \( f''(x) - 3a f'(x) - f(x) = 0 \), where \( a > 0 \), then the area of the region R = {(x, y) | 0 \(\leq\) y \(\leq\) f(ax), 0 \(\leq\) x \(\leq\) 2\ is :
If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then \( f(1) \) is: