ABCD-parallelogram. Find the length of the AC vector if the vector BA = (0; 2; 3) and the vector BD = (1; 4; 5).

| July 9, 2021 | education

Since ABCD is a parallelogram, the vectors lying on its opposite sides are collinear, that is, they are equal in absolute value. To find the length of the vector AC, it is necessary to express the coordinates of this vector in terms of the coordinates of other vectors. The AC vector is equal to the sum of the AD and DC vectors. Vector AD is equal to the difference between vectors BD and BA. It turns out that the vector AC is equal to the sum of the vectors AD and DC or the difference of the vectors AD and BA. It is known from the problem statement that the vector BA = (0; 2; 3), and the vector BD = (1; 4; 5), then the vector AC = (1; 4; 5) – (0; 2; 3) – ( 0; 2; 3); AC = (1; 0; – 1). The length of the vector AC is found by the formula | AC | = √ (x ^ 2 + y ^ 2 + z ^ 2); | AU | = √ (1 ^ 2 + 0 ^ 2 + (- 1) ^ 2); | AU | = √2.
Answer: the length of the AC vector is √2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.