If a unit vector `"a"` makes an angle `"pi"/3` with ` hat"i"," ""pi"/4` with ` hat"j"` and an acute angle `"theta"` with ` hat"k",` then find the value of `"theta"dot`

Explanation

`overline{r} cdot bar{n}_{1}={d}_{1}` and `overline{{r}} cdot bar{n}_{2} {~d}_{2}` is we have


`
cos theta=|frac{bar{n}_{1} cdot bar{n}_{2}}{|bar{n}_{1}||bar{n}_{2}|}| quad ldots(1)
`


`bar{n}_{1}=hat{i}+hat{j}+2 hat{k}, `


`bar{n}_{2}=2 hat{i}-hat{j}+hat{k} `


`therefore bar{n}_{1} cdot bar{n}_{2} `


`=(hat{i}+hat{j}+2 hat{k}) cdot(2 hat{i}+hat{j}+hat{k}) `


...