Question

The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is ______.

Answer 1

The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vec"r" = (5hat"i" - 4hat"j" + 6hat"k") + lambda(3hat"i" + 7hat"j" + 2hat"k")`.

Explanation:

The given equation is `(x - 5)/3 = (y + 4)/7 = (z - 6)/2`

Here `vec"a" = (5hat"i" - 4hat"j" + 6hat"k")` and `vec"b" = (3hat"i" + 7hat"j" + 2hat"k")`

Equation of the line is `vec"r" = vec"a" + vec"b"lambda`

Hence, the vector equation of the given line is `vec"r" = (5hat"i" - 4hat"j" + 6hat"k") + lambda(3hat"i" + 7hat"j" + 2hat"k")`