Find the angle between line `(x+1)/2=y/3=(z-3)/6` and the plane `10x+2y-11z-3=0.`

Explanation

Given `vecb=2hati+3hatj+6hatk` and `vec n=10hat+2hatj-11hatk`

We know,

`sin theta=frac{vecbcdotvecn}{|vecb|cdot|vecn|}`

`=frac{(2hati+3hatj+6hatk)cdot(10hati+2hatj-11hatk)}{|2hati+3hatj+6hatk|cdot|10hati+2hatj-11hatk|}`

`=frac{20+6-66}{sqrt{4+9+36}sqrt{100+4+121}}`

`=frac{-40}{sqrt{49}sqrt{225}`

`=frac{-40}{7times15}`

`=frac{-8}{21}`

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