# Mixing de IITJEE Problèmes...

Level pending

Consider the lines

$$L_{1}$$ : $$\frac{x+1}{3}$$ = $$\frac{y+2}{1}$$ = $$\frac{z+1}{2}$$

&

$$L_{2}$$ : $$\frac{x-2}{1}$$ = $$\frac{y+2}{2}$$ = $$\frac{z-3}{3}$$

(Following Equations Represents Equation of Line In 3 Dimensional Cartesian Coordinate System)

If the unit vector perpendicular to both $$L_{1}$$ and $$L_{2}$$ can be written as

$$\frac{a\hat{i}-b\hat{j}+c\hat{k}}{d\sqrt{e}}$$ ; where $$\hat{i}, \hat{j}, \hat{k}$$ are unit vectors along x-axis, y-axis, z-axis respectively and a,b,c,d,e $$\in$$ R

*Now if $$f(x)$$a function which is differentiable and *

$$\int_0^{t^{2}}xf(x)dx$$ = $$\frac{2}{5}t^{5}$$

then $$f(\frac{e-a}{cd}$$) = $$\frac{\alpha}{\beta}$$

where $$\beta > \alpha$$

Then value of $$1 + \omega^{\alpha + \beta} + \omega^{2b}$$ =

(Where $$\omega$$ is imaginary cube root of unity)

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