Given vectors: a {1; -4}; b {-4; 8}. find the absolute value of the vector with equal to the sum of a and b.

The coordinates of the sum of vectors are equal to the sums of the corresponding coordinates of the given vectors. If vector c is equal to the sum of vectors a and b, then its coordinates are respectively equal:

x = 1 + (-4) = -3,

y = -4 + 8 = 4.

The absolute value of a vector is equal to the root of the sum of the squares of its coordinates. Hence, the absolute value of the vector c is equal to:

√ ((- 3) ^ 2 + 4 ^ 2 = √ (9 + 16) = √ (25) = 5.