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

Explanation

We have given the equation of a line as `(x-5)/3=(y+4)/7=(z-6)/2`

Then we have to find vector equation of the above equation

Now as here the given line passes through point (5,-4,6) and has direction ratios proportional to (3,7,2)

Then vector equation can be given by

`vec(r)=vec(a)+lambda vec(b)`

Here `vec(a)=5hat(i)-4hat(j)+6hat(k)` and `vec(b)=3hat(i)+7hat(j)+2hat(k)`

`implies vec(r)=5hat(i)-4hat(j)+6hat(k)+ lambda (3hat(i)+7hat(j)+2hat(k))`