Question

The three planes 4y + 6z = 5; 2x + 3y + 5z = 5; 6x + 5y + 9z = 10

• A. meet in a point
• B. have a line in common
• C. form a triangle prism
• D. have exactly three solutions in common

Answer 1

The correct option is B have a line in common

If DC’s of line of intersection of planes
4y + 6z = 5 and 2x + 3y + 5z = 5
are l, m, n
$\therefore$ 0 + 4m + 6n = 0
2l + 3m + 5n = 0

$\Rightarrow$ $\frac{l}{1}=\frac{m}{6}=\frac{n}{-4}=\frac{1}{\sqrt{53}}$
$\Rightarrow$ $l=\frac{1}{\sqrt{53}},m=\frac{6}{\sqrt{53}},n=\frac{4}{\sqrt{53}}Also,6\left(\frac{1}{\sqrt{53}}\right)+5\left(\frac{6}{\sqrt{53}}\right)+9(-\frac{4}{\sqrt{53}})=0$