Question

-5/2(вектор AB+вектор BC-1/2вектораAC)

Answer 1

$\bar{AB}+\bar{BC}=\bar{AC}$

$\bar{AC}- (1/2)\cdot \bar{AC}=(1/2)\bar{AC}\\(-5/2)\cdot (1/2)\bar{AC}=(-5/4)\bar{AC}$

Answer 2

To compute the expression, let's break it down step by step:

1. Calculate the vector expressions:

   • Vector AB: This represents the vector from point A to point B.
   • Vector BC: This represents the vector from point B to point C.
   • Vector AC: This represents the vector from point A to point C.

2. Subtract 1/2 times vector AC from the sum of vector AB and vector BC.

3. Multiply the entire resulting vector by -5/2.

Let's assume that the vectors AB, BC, and AC are represented as 2D vectors in the form (x, y).

Expression: -5/2 * (AB + BC - 1/2 * AC)

Note: When adding and subtracting vectors, we perform vector addition and subtraction component-wise.

Example: Let's say vector AB = (3, 2), vector BC = (1, 4), and vector AC = (5, 1).

Calculation:

1. AB + BC = (3, 2) + (1, 4) = (4, 6)
2. 1/2 * AC = 1/2 * (5, 1) = (2.5, 0.5)
3. Subtract 1/2 * AC from the sum: (4, 6) - (2.5, 0.5) = (1.5, 5.5)
4. Multiply the resulting vector by -5/2: -5/2 * (1.5, 5.5) = (-7.5, -27.5)

So, the final result is the vector (-7.5, -27.5).