Given the vectors u with rightwards arrow on top equals open angle brackets short dash 3 comma space short dash 2 close angle brackets and v with rightwards arrow on top equals open angle brackets 5 comma space short dash 7 close angle brackets, find 4 u with rightwards arrow on top minus 2 v with rightwards arrow on top.

To find \( 4\vec{u} - 2\vec{v} \), we need to multiply each vector by its scalar and then subtract them.

### Given:
\[
\vec{u} = \langle -3, -2 \rangle, \quad \vec{v} = \langle 5, -7 \rangle
\]

### Step 1: Multiply \( \vec{u} \) by 4
\[
4\vec{u} = 4 \times \langle -3, -2 \rangle = \langle 4 \times (-3), 4 \times (-2) \rangle = \langle -12, -8 \rangle
\]

### Step 2: Multiply \( \vec{v} \) by 2
\[
2\vec{v} = 2 \times \langle 5, -7 \rangle = \langle 2 \times 5, 2 \times (-7) \rangle = \langle 10, -14 \rangle
\]

### Step 3: Subtract \( 2\vec{v} \) from \( 4\vec{u} \)
\[
4\vec{u} - 2\vec{v} = \langle -12, -8 \rangle - \langle 10, -14 \rangle = \langle -12 - 10, -8 - (-14) \rangle = \langle -22, 6 \rangle
\]

Thus, \( 4\vec{u} - 2\vec{v} = \langle -22, 6 \rangle \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you calculate the magnitude of a vector?
2. What is the dot product of \( \vec{u} \) and \( \vec{v} \)?
3. How do you find the angle between two vectors?
4. What is the geometric interpretation of vector subtraction?
5. How do you add two vectors graphically?

**Tip**: When working with vectors, always be mindful of signs during scalar multiplication and vector operations.

Given the vectors u⃗ = ⟨−3,−2⟩ and v⃗ = ⟨5,−7⟩, find 4u⃗ − 2v⃗.

Learn how to find 4u - 2v for the vectors u = ⟨-3, -2⟩ and v = ⟨5, -7⟩. This step-by-step solution covers vector algebra concepts like scalar multiplication and vector subtraction. Suitable for high school students in Grades 10-12.

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