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Question
Choose correct alternatives:
The vector equation of line 2x – 1 = 3y + 2 = z – 2 is ______.
Options
`barr = (1/2hati - 2/3hatj + 2hatk) + lambda(3hati + 2hatj + 6hatk)`
`barr = hati - hatj + (2hati + hatj + hatk)`
`barr = (1/2hati - hatj) + lambda(hati - 2hatj + 6hatk)`
`barr = (hati + hatj) + lambda(hati - 2hatj + 6hatk)`
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Solution
The vector equation of line 2x – 1 = 3y + 2 = z – 2 is `bb(underline(barr = (1/2hati - 2/3hatj + 2hatk) + lambda(3hati + 2hatj + 6hatk))`
Explanation:
2x − 1 = 3y + 2 = z − 2
We need to convert this into vector form of a line:
`vecr = veca+lambdavecb`
`2x - 1 = lambda => x = (lambda+1)/2`
`3y + 2 = lambda => y = (lambda-2)/3`
z − 2 = λ ⇒ z = λ + 2
`x = 1/2 + lambda/2, y = -2/3+lambda/3, z = 2 +lambda`
`vecr = veca + lambdavecb`
`vecb= 3hati + 2hatj + 6hatk`
`vecr = (1/2hati - 2/3hatj + 2hatk) + lambda(3hati + 2hatj + 6hatk)`
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