Show that the plane whose vector equation is ` vec r*( hat i+2 hat j= hat k)=3` contains the line whose vector equation is ` vec r*( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot`

Explanation

We have:

`r.(i+2j​−k)=3 ....(i)`

Normal vector `=n`

`=(i+2j​−k)`

Equation of line is

`r=i^+j^​+λ(2i^+j^​+4k^)`

Direction ratio `=m=2i+j​+4k`

`m.n=(2i+j​+4k).(i+2j​−k)=2+2−4=0`

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