Question

Дано: Вектор а перпендикулярен вектору b. |a|= 5, |b|= 12. Найти: |a+b|, |a-b|

Answer 1

|a|+|b|=17 |a|-|b|=-7

Answer 2

Given Information:

We are given that vector a is perpendicular to vector b and that the magnitudes of a and b are |a| = 5 and |b| = 12, respectively.

Finding |a + b| and |a - b|:

To find the magnitudes of a + b and a - b, we need to perform vector addition and subtraction, respectively, and then calculate their magnitudes.

1. Vector Addition: To find a + b, we add the corresponding components of a and b:

a + b = (a_x + b_x, a_y + b_y, a_z + b_z)

Since a is perpendicular to b, their corresponding components will be additive inverses of each other. Therefore, the resulting vector a + b will have zero components in the x, y, and z directions.

Thus, a + b = (0, 0, 0)

The magnitude of a + b is therefore |a + b| = sqrt(0^2 + 0^2 + 0^2) = 0

2. Vector Subtraction: To find a - b, we subtract the corresponding components of b from a:

a - b = (a_x - b_x, a_y - b_y, a_z - b_z)

Since a is perpendicular to b, their corresponding components will be additive inverses of each other. Therefore, the resulting vector a - b will have the same components as a.

Thus, a - b = (a_x, a_y, a_z)

The magnitude of a - b is therefore |a - b| = sqrt((a_x)^2 + (a_y)^2 + (a_z)^2)

Since a is perpendicular to b, the components of a will be perpendicular to each other. Therefore, (a_x)^2 + (a_y)^2 + (a_z)^2 = |a|^2 = 5^2 = 25.

Thus, |a - b| = sqrt(25) = 5

Summary:

The magnitudes of a + b and a - b are |a + b| = 0 and |a - b| = 5, respectively.