Question

The equation of the plane passing through the points (3,2, -1), (3, 4, 2) and (7, 0, 6) is 5x + 3y – 2z =k , then K 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, $5x+3y-2z=23$
$\therefore K=23$