Question

Lines x/2 = y/1 = z/3 and x-2/2 = y+1/1 = 3-z/-3 are.... lines.Select the correct option from the given options.
(a) parallel
(b) perpendicular
(c) coincident
(d) intersecting in an acute angle

Answer 1

for solution refer attachment and answer is option a

Answer 2

if equation of two lines are given (x - x1)/a1 = (y - y1)/b1 = (z - z1)/c1 and (x - x2)/a1 = (y - y1)/b1 = (z - z1)/c1

i) lines are parallel when , a1/a2 = b1/b2 = c1/c2
ii) lines are perpendicular when, a1a2 + b1b2 + c1c2 = 0

here lines are x/2 = y/1 = z/3
and (x - 2)/2 = (y + 1)/1 = (3 - z)/-3
or, (x - 2)/2 = (y + 1)/1 = (z - 3)/3

we see, 2/2 = 1/1 = 3/3
hence, lines are parallel .
therefore, option (a) is correct.