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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
  1. 23
  2. 27
  3. 21
  4. 19


Solution

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
∣ ∣x3y2z+1023427∣ ∣=0
We get,         5x+3y2z=23
K=23

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