Answer: r = a + lambda*(b-a) + mu*(c-a).
- A r . (b x c) = 0, a condition for a plane through the origin
- B r = (a+b+c)/3, just the centroid point
- C r = lambda*a + mu*b, missing the third point c
- D r = a + lambda*(b-a) + mu*(c-a)
Correct answer: D. r = a + lambda*(b-a) + mu*(c-a)
Explanation: The plane through a, b, c contains two direction vectors (b−a) and (c−a). Parametric form: r = a + λ(b−a) + μ(c−a), where λ,μ∈ℝ. When λ=μ=0: r=a; λ=1,μ=0: r=b; λ=0,μ=1: r=c. Answer: r = a + λ(b−a) + μ(c−a).
Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.
Concept context
Vectors, dot product, cross product, and geometric applications