Show plane whose vector equation is` vecrcdot(hati +2hatj-hatk)=3`contains the line `vecr=hati+j+lambda(2hati +hatj+4hatk)`

Explanation

Normal Vector `=vecn=(hati +2hatj-hatk)`

Equation of line is, `vecr=hati+hatj+lambda(2hati+hatj+4hatk)`

Direction ratio`=vecm=2hati+hatj+4hatk`

`vecmcdotvecn=(2hati+hatj+4hatk)cdot(hati +2hatj-hatk)`

`impliesvecmcdotvecn=0`

`hati+hatj` must satisfy equation of plane`

L.H.S.=vecr(hati +2hatj-hatk)`

`=(hati+hatj)cdot(hati +2hatj-hatk)`

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