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

Explanation

Equation of line
`(x-6)/(2)=(y+4)/(7)=(z-5)/(3)`
`therefore `The line is passing through the point `(6,-4,5)` and having direction ratios `2, 7, 3.`
`"so "veca=6hati - 4hatj+5hatk`
`"and "vec b=2hati+7hatj+3hatk`
`therefore "The vector eqaution of line is " vecr=veca+lambda vecb`
`rarr vecr = (6hati-4hatj+5hatk)+lambda(2hati+7hatj+3hatk)`