Vector Algebra

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(i)	Two rays in the first quadrant $x+y=|a|$ and $a x-y=1$ Intersects each other in the interval $a \in\left(a_0, \infty\right)$, the value of $a_0$ is	(A)	2
(ii)	Point $(\alpha, \beta, \gamma)$ lies on the plane $x+y+z=2$. Let $\vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}, \hat{k} \times(\hat{k} \times \vec{a})=0$, then $\gamma=$	(B)	4/3
(iii)	\( \left|\int_0^1\left(1-y^2\right) d y\right|+\left|\int_1^0\left(y^2-1\right) d y\right| \)	(C)	\( \left|\int_0^1 \sqrt{1-x} d x\right|+\left|\int_1^0 \sqrt{1+x} d x\right| \)
(iv)	If $\sin A \sin B \sin C+\cos A \cos B=1$, then the value of $\sin C=$	(D)	1