Find the vector equation of line passing through `A(3,4-7)a n dB(1,-1,6)dot` Also find its Cartesian equations.

Explanation

Since the line passes through `A(3hati+4hatj-7hatk) and B(hati-hatj+6hatk)`, its vector equation is
`" "vecr=3hati+4hatj-7hatk+lamda[(hati-hatj+6hatk)-(3hati+4hatj-7hatk)]`
`" "=3hati+4hatj-7hatk-lamda(2hati+5hatj-13hatk)" "`(i)
where `lamda` is a parameter.
The Cartesian equivalent of (i) is `(x-3)/(2)=(y-4)/(5)=(z+7)/(-13)`.