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Question
Verify if the point having position vector `4hat"i" - 11hat"j" + 2hat"k"` lies on the line `bar"r" = (6hat"i" - 4hat"j" + 5hat"k") + lambda (2hat"i" + 7hat"j" + 3hat"k")`
Solution
`bar"r" = (6hat"i" - 4hat"j" + 5hat"k") + lambda (2hat"i" + 7hat"j" + 3hat"k")`
Replacing `bar"r"` by `4hat"i" - 11hat"j" + 2hat"k"`, we get
`4hat"i" - 11hat"j" + 2hat"k" = 6hat"i" - 4hat"j" + 5hat"k" + lambda(2hat"i" + 7hat"j" + 3hat"k")`
∴ 6 + 2lambda = 4, – 4 + 7λ
= – 11, 5 + 3λ
= 2
From each of these equations, we get the same value of λ.
∴ The given point lies on the given line.
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