The vector equation of the plane passing through vector a, vector b, vector c is vector r = α vector a + β vector b + γ vector c, provided that

Question

The vector equation of the plane passing through  \(\vec a,\,\vec b,\,\vec c\)  is  \(\vec r\) = α \(\vec a\) + β \(\vec b\) + γ \(\vec c\), provided that

A. α + β + γ = 0

B.α + β + γ = 1

C. α + β = γ

D. α² + β² + γ² = 1

Answer 1

 Correct option is B.α + β + γ = 1

As a plane passing through  \(\vec a,\,\vec b, \,\vec c \).

Lines  \(\vec a-\vec b\) and  \(\vec c-\vec a\) lie on the plane.

The parametric equation of the plane can be expressed as,