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Question
The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is ______.
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Solution
The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vecr = 5hati - 4hatj + 6hatk + lambda(3hati + 7hatj + 2hatk)`.
Explanation:
We have, `(x - 5)/3 = (y + 4)/7 = (z - 6)/2`
The given line passes through the point (5, - 4 , 6 ) and has direction ratios proportional to 3, 7, 2.
Vector equation of the given line passing through the point having position vector
`veca = 5hati - 4hatj + 6hatk` and parallel to a vecto `vecb = 3hati + 7hatj + 2hatk` is `vecr = veca + lambdavecb`
⇒ `vecr = 5hati - 4hatj + 6hatk + lambda(3hati + 7hatj + 2hatk)`
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