https://file.aiquickdraw.com/mathbot/file/1725986374993rnoei7jn.jpg

The problem provided asks to find \( 2\vec{g} - 2\vec{h} \), where:

\[
\vec{g} = \langle 3, -5 \rangle \quad \text{and} \quad \vec{h} = \langle -2, 3 \rangle
\]

Let's compute step by step:

1. First, calculate \( 2\vec{g} \):
   \[
   2\vec{g} = 2 \times \langle 3, -5 \rangle = \langle 2 \times 3, 2 \times (-5) \rangle = \langle 6, -10 \rangle
   \]

2. Next, calculate \( 2\vec{h} \):
   \[
   2\vec{h} = 2 \times \langle -2, 3 \rangle = \langle 2 \times (-2), 2 \times 3 \rangle = \langle -4, 6 \rangle
   \]

3. Now, subtract \( 2\vec{h} \) from \( 2\vec{g} \):
   \[
   2\vec{g} - 2\vec{h} = \langle 6, -10 \rangle - \langle -4, 6 \rangle = \langle 6 - (-4), -10 - 6 \rangle = \langle 10, -16 \rangle
   \]

Thus, the answer is \( \langle 10, -16 \rangle \), which corresponds to option A.

Would you like further details or have any questions?

Here are some related questions you might explore:
1. How do you add and subtract vectors geometrically?
2. What is the significance of scalar multiplication in vectors?
3. How do you represent vectors in terms of their magnitude and direction?
4. How can vector operations be applied in physics?
5. What is the difference between a vector and a scalar quantity?

**Tip:** Always ensure that vector operations respect the order of the components when adding or subtracting.

Given g⃗=⟨3,−5⟩ and h⃗=⟨−2,3⟩, find 2g⃗−2h⃗.

Learn how to calculate the result of 2g⃗−2h⃗ for the vectors g⃗=⟨3,−5⟩ and h⃗=⟨−2,3⟩. This problem involves vector scalar multiplication and subtraction, with a step-by-step solution suitable for students in Grades 9-12.

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