Question

The Cartesian equations of a line are `(x-1)/(2)=(y+2)/(3) =(z-5)/(-1)` . Its vector equations is
A. `vec(r ) =(-hat(i) +2hat(j) -5hat(k)) + lambda (2hat(i) +3hat(j) -hat(k))`
B. `vec(r )=(2hat(i) +3hat(j) -hat(k)) +lambda (hat(i)-2hat(j) +5hat(k))`
C. `vec(r )=(hat(i) -2hat(j) +5hat(k)) +lambda (2hat(i) +3hat(j)-4hat(k))`
D. none of these

Answer 1

Correct Answer - C
The line passes through the point `(1-2,5)`and it has direction rations 2,3,-1
So, it vector equations is `vec(r ) =(hat(i) -2hat(j) +5hat(k)) +lambda (2hat(i) +3hat(j) -hat(k))`