Given points A (3; -2), B (7; 5), M (-5; 7), N (2; -4). Find the dot product of vectors AB and MN

Given points A (3; -2), B (7; 5), M (-5; 7), N (2; -4). Find the dot product of vectors AB and MN and determine whether these vectors are perpendicular

Knowing the coordinates of points A, B, M and N, we can find the coordinates of vectors AB and MN:

AB = {7 – 3; 5 – (-2)} = {7 – 3; 5 + 2} = {4; 7};

MN = {2 – (-5); -4 – 7} = {2 + 5; -4 – 7} = {7; -eleven}.

Knowing the coordinates of the vectors AB and MN, we can find what the scalar product of these vectors is equal to:

AB * MN = 4 * 7 + 7 * (-11) = 28 – 77 = -49.

Since the scalar product of vectors AB and MN is nonzero, these vectors are not perpendicular.

Answer: the dot product of vectors AB and MN is -49, these vectors are not perpendicular.