Question

The point of intersection of the line joining the points (3, 4, 1) and (5, 1, 6) and the xy-plane is

• A. $( 13,23,0 )$
• B. $\left( \frac { 13 } { 5 } , \frac { 23 } { 5 } , 0 \right)$
• C. (–13, 23, 0)
• D. $\left( - \frac { 13 } { 5 } , \frac { 23 } { 5 } , 0 \right)$

Answer 1

Answer: (B)

$\left( \frac { 13 } { 5 } , \frac { 23 } { 5 } , 0 \right)$

Answer 2

For xy-plane, $z = 0 \Rightarrow \frac { 6 \lambda + 1 } { \lambda + 1 } = 0 \Rightarrow \lambda = - \frac { 1 } { 6 }$

$\therefore x = \frac { - 5 + 18 } { 5 } = \frac { 13 } { 5 } , y = \frac { - 1 + 24 } { 5 } = \frac { 23 } { 5 }$ .