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Question
The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is ______.
Solution
The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is `3hati + 4hatj - 7hatk + lambda|-2hati - 5hatj + 13hatk|`.
Explanation:
Given points are A(3, 4, –7), B(1, –1, 6)
`vecA = 3hati + 4hatj - 7hatk`
`vecB = hati - hatj + 6hatk`
∴ Vector equation
`vecr = (3hati + 4hatj - 7hatk) + lambda[hati - hatj + 6hatk - (3hati + 4hatj - 7hatk)]`
= `3hati + 4hatj - 7hatk + lambda[-2hati - 5hatj + 13hatk]`
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