question_answer 1)

Find the equation of the planes that pass through the sets of three points (a) (1, 1, –1), (6, 4, –5), (–4, –2, 3) (b) (1, 1, 0), (1, 2, 1), (–2, 2, –1)  

Answer:

We know that equation of plane passing through points A (x1, y1, z1) and C(x3, y3, z3) is       (a)   Therefore, equation of plane passing through points (1, 1, ?1), (6, 2, ?5) and (?4, ?2, 3) is given by                                                 (By taking ?1 as common from R3)             [ Rows R2 and R3 are identical]        given points are collinear. So there are infinite number of planes passing through the given points.       (b) Equation of plane passing through the points (1, 1, 0), (1,2, 1) and (?2, 2, ?1) is given by