Find the Cartesian equations of the line which passes through the point (1,3-2) and is parallel to the given by ltbgt `(x+1)/(3) =(y-4)/(5)=(z+3)/(-6)

Correct Answer - B `vecr=(-hati+3hatj+5hatk)+lambda(2hati+3hatj)`

Correct Answer - `vec(r )=(2hat(i)+4hat(j)+5hat(k)) +lambda(2hat(i) +2hat(j)-3hat(k)) ,(x-3)/(2)=(y-4)/(2)=(z-5)/(-3)`

Correct Answer - `vec(r )=(2hat(i)-hat(j)-3hat(k)) +lambda (hat(i) -2hat(j)+3hat(k)) ,(x-2)/(1)=(y-1)/(-2)=(z+3)/(3)`

Correct Answer - `vec(r ) =(2hat(i) +hat(j) -5hat(k)) +lambda(hat(i) +3hat(j)-hat(k)) ,(x-2)/(1)=(y-1)/(3)=(z+5)/(-1)`

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

Correct Answer - `(x-1)/(3)=(y+2)/(-4) =(z-3)/(5) , vec( r) =(hat(i) -2hat(j) +3hat(k)) +lambda (3hat(i) -4hat(j) +5hat(k))`

Correct Answer - `(x-1)/(2)=(y-2)/(3)=(z+4)/(6),vec(r ) =(hat(i) +2hat(j) -4hat(k)) +lambda(2hat(i) +3hat(j) +6hat(k))`

Correct Answer - (i)4x-y=27=0 (ii)3x+y+3=0 (iii)`sqrt3+y-2=0`

Correct Answer - x-y-8=0

Correct Answer - 3x-5y+25=0