If $A$ and $B$ are events such that $P(A / B)=P(B / A) \neq 0$, then

Assertion (A): Domain of $y=\cos ^{-1}(x)$ is $[-1,1]$.

Reason ( R ): The range of the principal value branch of $y=\cos ^{-1}(x)$ is $[0, \pi]-\left\{\frac{\pi}{2}\right\}$

Assertion (A): The vectors

$$\begin{aligned} & \vec{a}=6 \hat{i}+2 \hat{j}-8 \hat{k} \\ & \vec{b}=10 \hat{i}-2 \hat{j}-6 \hat{k} \\ & \vec{c}=4 \hat{i}-4 \hat{j}+2 \hat{k} \end{aligned}$$

represent the sides of a right angled triangle.

Reason (R): Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

Find value of $k$ if $\sin ^{-1}\left[k \tan \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right]=\frac{\pi}{3}$.