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Question
Find the vector equation of the plane passing through the point having position vector `hati + hatj + hatk` and perpendicular to the vector `4hati + 5hatj + 6hatk`.
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Solution
Let position vector of point A be `veca`
`veca = hati + hatj + hatk`,
also `vecn = 4hati + 5hatj + 6hatk`
∴ `veca.vecn = (hati + hatj + hatk).(4hati + 5hatj + 6hatk)`
= (1)(4) + (1)(5) + (1)(6)
= 4 + 5 + 6
= 15 ....(1)
∴ The vector equation of plane is
`vecr.vecn = veca.vecn`
`vecr.(4hati + 5hatj + 6hatk)` = 15 ...[From 1]
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