Question

The point of intersection of line, passing through (0, 0, 1) and intersecting lines x + 2y + z = 1,

–x + y –2z = 2 and x + y = 2, x + z = 2 with xy plane is-

• A. $\left( \frac{5}{3},\frac{- 1}{3},0 \right)$
• B. (1, 1, 0)
• C. $\left( \frac{2}{3},\frac{- 1}{3},0 \right)$
• D. $\left( \frac{- 5}{3},\frac{- 1}{3},0 \right)$

Answer 1

Answer: (A)

$\left( \frac{5}{3},\frac{- 1}{3},0 \right)$

Answer 2

Equation of line is

x + 2y + z –1 + l (–x + y –2z –2) = 0

& x + y – 2 + m(x + z –2) = 0

put (0, 0, 1)

\ l = 0, m = –2

for point of intersection put z = 0