Question

Let a, b and c be three non-zero vectors, no two of which are collinear. If the vector a + 2b is collinear with c, and b + 3c is collinear with a, then a + 2b + 6c is equal to ( λ being some non-zero scalar) then a + 2b + 6c =

A. λa
B. λb
C. λc
D. o

Answer 1

The vector equation a + 2b + 6c, given the collinearity conditions for a + 2b with c, and b + 3c with a, results in every term having c as a factor. Thus the final vector is a scalar multiple of c, specifically λc. The correct answer is C. λc.

Step-by-step explanation:

The question asks about the vector equation a + 2b + 6c, given the two conditions that a + 2b is collinear with c, and b + 3c is collinear with a. To be collinear, one vector must be a scalar multiple of the other. This means there exist scalars λ and μ such that:

• a + 2b = λc
• b + 3c = μa

Expressing the vectors a and b in terms of c from these equations and substituting back into the original equation a + 2b + 6c, we find that every term will have c as a factor, leading to the final vector being a multiple of c. Therefore, the answer to the initial question is:

a + 2b + 6c = λc

where λ is a non-zero scalar. Thus, the correct option is C. λc.