The sides of a regular triangle ABC are equal to 2√3. Find the length of the vector ab + ac.

Draw a triangle to a parallelogram, or in our case to a rhombus abcd, since the sides are equal.

Let’s add two vectors according to the parallelogram rule.

The length of the larger diagonal ad will be the length of the required vector.

Let us find the length of the larger diagonal ad, knowing the length of the smaller diagonal bc = d, using the following formula:

Ad = D = (4 * (ab) ^ 2 – d ^ 2) ^ (1/2) = (4 * (2√3) ^ 2 – (2√3) ^ 2) ^ (1/2) = (3 * 4 * 3) ^ (1/2) = 3 * 2 = 6.

Answer: the length of the sum of vectors ab + ac is 6.