Given vector v, equals, open angle bracket, 1, comma, 2, close angle bracket, commav=⟨1,2⟩, find 6, v, .6v.

Given the vector \( \mathbf{v} = \langle 1, 2 \rangle \), we want to find \( 6\mathbf{v} \).

To do this, we multiply each component of the vector by 6:

\[
6\mathbf{v} = 6 \times \langle 1, 2 \rangle = \langle 6 \times 1, 6 \times 2 \rangle = \langle 6, 12 \rangle
\]

Thus, \( 6\mathbf{v} = \langle 6, 12 \rangle \).

Would you like any further details or explanations on vector scaling or vector operations?

Here are 5 questions for further practice:
1. What is \( 3\mathbf{v} \) if \( \mathbf{v} = \langle 1, 2 \rangle \)?
2. How do you find the magnitude of the vector \( \mathbf{v} \)?
3. What is the direction of the vector \( 6\mathbf{v} \)?
4. If \( \mathbf{v} = \langle 1, 2 \rangle \), what is \( -2\mathbf{v} \)?
5. What is the result of adding two vectors, \( \mathbf{v}_1 = \langle 3, 4 \rangle \) and \( \mathbf{v}_2 = \langle 1, 2 \rangle \)?

**Tip:** When scaling a vector, every component is multiplied by the same scalar, keeping the direction the same unless the scalar is negative.

Learn how to scale a vector by a scalar with this detailed example. Find 6v for vector v = ⟨1, 2⟩ by multiplying each component of the vector by 6. This concept covers vector operations and scalar multiplication, suitable for students in Grades 9-11.

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