A man is known to speck truth 3 out of 4 times. He throws a die and reports that it is 6. Then the probability that it is actually 6 is

If $$\bar{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \bar{b}=-\hat{i}+2 \hat{j}-4 \hat{k}$$ and $$\bar{c}=\hat{i}+\hat{j}-2 \hat{k}$$, then $$(\bar{a} \times \bar{b}) \cdot(\bar{a} \times \bar{c})=$$

The differential equation obtained by eliminating A and B from $$y=A \cos \omega t+B \sin \omega t$$

The Cartesian equation of a plane which passes through the points $$\mathrm{A}(2,2,2)$$ and making equal nonzero intercepts on the co-ordinate axes is