Find a vector ` vec r` of magnitude `3sqrt(3)u n i t s` which makes an angle of `pi/4` and `pi/2` with `y` and `z-`axis respectively.

Explanation

`vec{r}=x hat{1}+y hat{j}+2 hat{k} `

`|vec{r}|=3 sqrt{2} `

`sqrt{x^{2}+y^{2}+z^{2}}=3 sqrt{2} `

`x^{2}+y^{2}+z^{2}=18`

It makes `frac{pi}{4}` with yours

So, `vec{r} cdot j=|vec{r}| cos frac{pi}{4}`

`y=frac{3 sqrt{2}}{sqrt{2}}=3`

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