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Question
The Cartesian equation of a line is `(x-5)/3 = (y+4)/7 = (z-6)/2` Write its vector form.
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Solution
The equation of the line is `(x - 5)/3 = (y + 4)/7 = (z - 6)/2`.
This line passes through the point (5, −4, 6) and its direction ratios are 3, 7, 2.
That is, `vec(r_1) = 5hati - 4hatj + 6hatk` and `vecb = 3hati + 7hatj + 2hatk`
Hence the vector equation of the line is `vecr = vec(r_1) + λ vecb`
= `(5hati - 4hatj + 6hatk) + λ(3hati + 7hatj + 2hatk)`
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