Question

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

Answer 1

Correct Answer - B
The line passes through the point `(2hat(i) - hat(j) +3hat(k))` and it is parallel to the vector
`(2hat(i) + 3hat(j) -2hat(k))`
So, its vector equations `vec(r ) = (2hat(i) - hat(j) +3hat(k)) + lambda (2hat(i) +3hat(j) -2hat(k))`