Question
Use the properties of vectors to solve the following equation for the unknown vector \( \mathbf{x}=\langle\mathrm{a}, \mathrm{b}\rangle \). Let \( \mathbf{u}=\langle-4,4\rangle \). \[ 10 \mathbf{x}=\mathbf{u} \] \( \mathrm{x}=\langle\square, \square \) (Simplify your answers. Type integers or a fractions.)
Ask by Fernandez Cummings. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\mathbf{x} = \left\langle -\dfrac{2}{5}, \dfrac{2}{5} \right\rangle
\]
Solution
To solve for the unknown vector \( \mathbf{x} = \langle a, b \rangle \) in the equation:
\[
10 \mathbf{x} = \mathbf{u} = \langle -4, 4 \rangle
\]
We can divide both components of the equation by 10:
\[
\mathbf{x} = \frac{\mathbf{u}}{10} = \left\langle \frac{-4}{10}, \frac{4}{10} \right\rangle
\]
Simplifying the fractions:
\[
\mathbf{x} = \left\langle -\frac{2}{5}, \frac{2}{5} \right\rangle
\]
**Answer:**
\[
\mathbf{x} = \left\langle\,-\dfrac{2}{5},\;\dfrac{2}{5}\,\right\rangle
\]
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Simplify this solution The Deep Dive
To solve for the unknown vector \( \mathbf{x} \), we start with the equation given: \[ 10 \mathbf{x} = \mathbf{u} \] Substituting the known vector \( \mathbf{u} = \langle -4, 4 \rangle \): \[ 10 \mathbf{x} = \langle -4, 4 \rangle \] Now, we need to isolate \( \mathbf{x} \) by dividing both sides of the equation by 10: \[ \mathbf{x} = \frac{1}{10} \langle -4, 4 \rangle \] This gives us: \[ \mathbf{x} = \langle \frac{-4}{10}, \frac{4}{10} \rangle \] Simplifying the fractions: \[ \mathbf{x} = \langle -\frac{2}{5}, \frac{2}{5} \rangle \] So the final answer is: \( \mathrm{x}=\langle -\frac{2}{5}, \frac{2}{5} \rangle \)
