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Find the vector equation of a plane whi...

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector `3 hat i+5 hat j-6 hat k`.

Text Solution

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Normal vector is ` vecn = 3hati+5hatj-6hatk`
unit normal vector on plane is `hatn = (vecn)/(|vecn|)`
`hatn =(3hati+5hatj-6hatk)/(sqrt(3^(2)+5^(2)+(-6)^(2)))`
`= (3hati+5hatj-6hatk)/(sqrt(70))`
`= (3)/(sqrt(70))hati+(5)/(sqrt(70))hatj-(6)/(sqrt(70))hatk`
Vector equation of a plane is `vecr.hatn = d`
`:. vecr.(3/(sqrt(70))hati+(5)/(sqrt(70))hatj-(6)/(sqrt(70))hatk) = 7`.
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