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Question
Find the non-parametric form of vector equation and Cartesian equations of the straight line passing through the point with position vector `4hat"i" + 3hat"j" - 7hat"k"` and parallel to the vector `2hat"i" - 6hat"j" + 7hat"k"`
Solution
`vec"a" = 4hat"i" + 3hat"j" - 7hat"k" (x_1, y_1, z_1)` = (4, 3, – 7)
`vec"b" = 2hat"i" - 6hat"j" + 7hat"k" (l, "m", "n")` = (2, – 6, 7)
Vector equation
`(vec"r" - vec"a") xx vec"b"` = 0
`[vec"r" - (4hat"i" + 3hat"j" - 7hat"k")] xx (2hat"i" - 6hat"j" + 7hat"k")` = 0
Cartesian equations
`(x - x_1)/l = (y - y_1)/"m" = (z - z_1)/"n"`
⇒ `(x - 4)/2 = (y - 3)/(-6) = (z + 7)/7`
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