Question

Дано: а̅(-8; у; 4); ∣а̅∣=10. Знайти: у.​

Answer 1

Ответ:

$\sqrt{ {( - 8)}^{2} + {y}^{2} + {4}^{2} } = 10 \\ \sqrt{64 + {y}^{2} + 16} = 10 \\ \sqrt{80 + {y}^{2} } = 10 \\ 80 + {y}^{2} = {10}^{2} \\ 80 + {y}^{2} = 100 \\ {y}^{2} = 100 - 80 \\ {y}^{2} = 20 \\ y = \sqrt{20} \\ y = 2 \sqrt{5}$

Answer 2

Дано: а̅(-8; у; 4) и ∣а̅∣=10. Нужно найти значение у.

Finding the Value of у

To find the value of у, we need to use the given information about the vector а̅ and its magnitude.

The magnitude of a vector is calculated using the formula: ∣а̅∣ = sqrt(x^2 + y^2 + z^2), where (x, y, z) are the components of the vector.

In this case, we have the vector а̅(-8, у, 4) and its magnitude ∣а̅∣ = 10.

Using the formula, we can set up the following equation: 10 = sqrt((-8)^2 + у^2 + 4^2)

Simplifying the equation, we get: 100 = 64 + у^2 + 16

Combining like terms, we have: у^2 = 100 - 64 - 16 у^2 = 20

Taking the square root of both sides, we find: у = ±√20

Therefore, the value of у can be either positive or negative square root of 20.

у = ±√20