Question

The equation of the plane passing through the line $\frac{x - 1}{5} = \frac{y + 2}{6} = \frac{z - 3}{4}$and the point (4, 3, 7) is

• A. $4x + 8y + 7z = 41$
• B. $4x - 8y + 7z = 41$
• C. $4x - 8y - 7z = 41$
• D. $4x - 8y + 7z = 39$

Answer 1

Answer: (B)

$4x - 8y + 7z = 41$

Answer 2

Any plane through given line is

$A ( x - 1 ) + B ( y + 2 ) + C ( z - 3 ) = 0$ .....(i)

and $5 A + 6 B + 4 C = 0$ …..(ii)

Since, plane (i) passes through (4, 3, 7), we get

$3 A + 5 B + 4 C = 0$ .....(iii)

Solving (ii) and (iii), we get $\frac { A } { 4 } = \frac { B } { - 8 } = \frac { C } { 7 }$

$\therefore$ Equation of required plane is $4 x - 8 y + 7 z = 41$ .