Question

Даны векторы c -1;5;2 и b 2;-3;1 найдите |c-2b|

Answer 1

С - 2b = (-1;5;2) - 2(2;-3;1) = (-1-2*2; 5+2*3; 2-2*1) = (-5;11;0)
|с - 2b| = √(5² + 11² + 0²) = √(25 + 121) = √146

Answer 2

To find the magnitude of the vector c - 2b, we first need to compute the vector c - 2b, and then find its magnitude.

Given: Vector c = (-1, 5, 2) Vector b = (2, -3, 1)

Step 1: Compute c - 2b To subtract two vectors, we subtract the corresponding components:

c - 2b = (-1 - 2*2, 5 - 2*(-3), 2 - 2*1) = (-1 - 4, 5 + 6, 2 - 2) = (-5, 11, 0)

Step 2: Find the magnitude of c - 2b The magnitude of a vector v = (x, y, z) is given by the formula:

|v| = sqrt(x^2 + y^2 + z^2)

So, for our vector c - 2b = (-5, 11, 0), the magnitude is:

|c - 2b| = sqrt((-5)^2 + 11^2 + 0^2) = sqrt(25 + 121) = sqrt(146) ≈ 12.083

Therefore, the magnitude of the vector c - 2b is approximately 12.083.