Question

The line passing through the points (5, 1, a) and (3, b, 1)  crosses the yz- plane at the point $\left(0,\frac{17}{2},\frac{-13}{2}\right)$ . Then;

• (A) a = 2, b = 8
• (B) a = 4, b = 6
• (C) a = 6, b = 4
• (D) a = 8, b = 6

Answer 1

The Correct Option is C

Explanation:
Given:The line passing through the points (5, 1, a) and (3, b, 1)  crosses the yz- plane at the point $\left(0,\frac{17}{2},\frac{-13}{2}\right)$We have to find values of a, b.We know, Equation of Line in Symmetrical Form passing through points (x1, y1, z1) and (x, y, z) is given by$\frac{x-x_2}{x_1-x_2}=\frac{y-y_2}{y_1-y_2}=\frac{z-z_2}{z_1-z_2}$ ...(i)Thus, the equation of line passing through $(5,1,a)$ and $(3,b,1)$ is$\frac{x-3}{5-3}=\frac{y-b}{1-b}=\frac{z-1}{a-1}$since the line passes through the point $(0,\frac{17}{2},\frac{-13}{2}).$$\therefore$ It satisfies equation (i),$\Rightarrow \frac{0-3}{2}=\frac{\frac{17}{2}-b}{1-b}=\frac{\frac{-13}{2}-1}{a-1}$$\Rightarrow \frac{-3}{2}=\frac{17-2b}{2-2b}=\frac{-15}{2a-2}$...(ii)For $\frac{-3}{2}=\frac{17-2b}{2-2b}[\text{ using (ii) }]$$\Rightarrow -6+6b=34-4b$$\Rightarrow 10b=40$$\Rightarrow \mathrm{b}=\frac{40}{10}=4$For $\frac{-3}{2}=\frac{-15}{2x-2}[\text{ using (ii) }]$$\Rightarrow -30=-6a+6$$\Rightarrow 6a=36$$\Rightarrow a=\frac{36}{6}=6$$\therefore a=6,b=4$Hence, the correct option is (C).