Question

Даны векторы: a=(2,3,0); b=(-6,0,1); c=(5,1,-1) Найти: 1) 2c-5a;

Answer 1

2c=(10,2,-2)
5a=(10,15,0)
2c-5a=(0,-13,-2)

Answer 2

To find the vector $2c - 5a$, we first need to perform scalar multiplication on each vector and then perform vector subtraction. Scalar multiplication involves multiplying each component of the vector by the scalar (a constant).

Given the vectors: $a = (2, 3, 0)$ $b = (-6, 0, 1)$ $c = (5, 1, -1)$

Let's calculate $2c - 5a$ step by step:

1. Calculate $2c$: $2c = 2 \cdot (5, 1, -1) = (2 \cdot 5, 2 \cdot 1, 2 \cdot -1) = (10, 2, -2)$

2. Calculate $5a$: $5a = 5 \cdot (2, 3, 0) = (5 \cdot 2, 5 \cdot 3, 5 \cdot 0) = (10, 15, 0)$

3. Perform vector subtraction: $2c - 5a = (10, 2, -2) - (10, 15, 0) = (10 - 10, 2 - 15, -2 - 0) = (0, -13, -2)$

So, the vector $2c - 5a$ is $(0, -13, -2)$.