Find the coordinates and length of the vector and if a = -b + 1 / 2c B {3; -2} c {-6; 2}.

Let there be given three vectors with coordinates a {x; y}; b {3; – 2} and c {- 6; 2}. It is known from the problem statement that the vector a has the following expansion in terms of basis vectors b and c: a = – b + (1/2) ∙ c. Then the coordinates of the vector a will be:

x = – 3 + (1/2) ∙ (- 6) = – 6;

y = – (- 2) + (1/2) ∙ 2 = 3.

Finally, we get that the coordinates of the vector a {- 6; 3}. Hence the length of the vector is:

| a | = √ ((- 6) ² + 3²) = √45 = 3 ∙ √5 ≈ 6.7.

Answer: vector a has coordinates {- 6; 3}, the length of the vector a is ≈ 6.7 unit segments.