1.

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

Answer» 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.


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