Найдите косинус угла между векторами (а+b) и (a-b) , если а {7;-1} ,b{5;5}

To find the cosine of the angle between two vectors, we can use the formula:

cos(theta) = (a · b) / (||a|| ||b||)

First, let's calculate the dot product of vectors a and b:

a · b = 7 * 5 + (-1) * 5 = 35 - 5 = 30

Next, let's calculate the magnitudes of vectors a and b:

||a|| = sqrt(7^2 + (-1)^2) = sqrt(49 + 1) = sqrt(50) = 5√2

||b|| = sqrt(5^2 + 5^2) = sqrt(25 + 25) = sqrt(50) = 5√2

Now, we can substitute these values into the formula:

cos(theta) = (a · b) / (||a|| ||b||) = 30 / (5√2 * 5√2) = 30 / (25 * 2) = 30 / 50 = 3/5

Therefore, the cosine of the angle between (a+b) and (a-b) is 3/5.