Question

The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane $x + 2y - 5z + 9 = 0$ is

• A. $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{- 5}$
• B. $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z + 5}{3}$
• C. $\frac{x + 1}{1} = \frac{y + 2}{2} = \frac{z + 3}{- 5}$
• D. $\frac{x + 1}{1} = \frac{y + 2}{2} = \frac{z - 5}{3}$

Answer 1

Answer: (A)

$\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{- 5}$

Answer 2

The line passes through point (1,2,3) is $\frac { x - 1 } { a } = \frac { y - 2 } { b } = \frac { z - 3 } { c }$ and it is perpendicular to the plane $x + 2 y - 5 z + 9 = 0$ therefore the line must be $\frac { x - 1 } { 1 } = \frac { y - 2 } { 2 } = \frac { z - 3 } { - 5 }$because $\sin \theta = \frac { 1 \cdot 1 + 2 \cdot 2 + ( - 5 ) ( - 5 ) } { \sqrt { 1 ^ { 2 } + 2 ^ { 2 } + 5 ^ { 2 } } \cdot \sqrt { 1 ^ { 2 } + 2 ^ { 2 } + 5 ^ { 2 } } } = 1$

$n = \frac { - 2 } { 3 }$.