Question

The equation of the plane passing through the points $(3,2,-1),(3,4,2)and(7,0,6)is5x+3y–2z=\lambda ,where\lambda$is

• A. 23
• B. 21
• C. 19
• D. 27

Answer 1

The correct option is A 23

Equation of plane through (3, 2, –1) is
a( x – 3) + b(y – 2) + c(z + 1) = 0 . . . .(i)
also (3, 4, 2) and (7, 0, 6) lie on Eq. (i), then
0 · a + 2b + 3c = 0 . . . .(ii)
and 4a – 2b + 7c = 0 . . . .(iii)
Eliminating a, b, c from Eqs. (i), (ii) and (iii), we get
$\left|\begin{array}{ccc}x-3& y-2& z+1\\ 0& 2& 3\\ 4& -2& 7\end{array}\right|=0$
We get, 5x + 3y – 2z = 23
$\lambda =23$