Write the vector equation of the following line: `(x-5)/3=(y+4)/7=(6-z)/2`

Explanation

Let `(x-5)/3 = (y+4)/7 = (6-z)/2 = lambda`

Then,

`=>x = 3lambda+5`

`=>y = 7lambda-4`

`=>z = -2lambda+6`

`:. vecr = xhati+yhatj+zhatk`

`=>vecr = (3lambda+5)hati+(7lambda-4)hatj+(-2lambda+6)hatk`

`=>vecr = (5hati-4hatj+6hatk)+lambda(3hati+7hatj-2hatk)`,which is the required vector equation.