The cartesian equation of a line is `(x-5)/3=(y+4)/7=(z-6)/2`. Write its vector form.

Explanation

Cartessian equation of the given line is
`(x-5)/(3) = (y+4)/(7) = (z-6)/(2)`
The line passes through the point `(5,-4,6)`. The position vector of this point is `veca = 5hati-4hatj+6hatk` and the direction ratio are 3,7 and 2, which mean sthe line is along the vector `vecb = 3hati+7hatj+2hatk`.
`:.` Vector equation of line
`:. vecr = 5hati-4hatj+6hatk+lambda(3hati+7hatj+2hatk)`