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Question
Find the vector equation of the line passing through points having position vector `3hati + 4hatj - 7hatk and 6hati - hatj + hatk`.
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Solution
The vector equation of the line passing through the `A(bara) and B(barb)` is
`vecr = bara + λ(barb - bara)`, λ is a scalar.
∴ The vector equation of the line passing through the points having position vector
`3hati + 4hatj - 7hatk and 6hati - hatj + hatk` is
`vecr = (3hati + 4hatj - 7hatk) + λ[(6hati - hatj + hatk) - (3hati + 4hatj - 7hatk)]`
i.e. `vecr = (3hati + 4hatj - 7hatk) + λ(3hati - 5hatj + 8hatk).`
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