Problem 28
Question
In Exercises \(21-38,\) let $$\mathbf{u}=2 \mathbf{i}-5 \mathbf{j}, \mathbf{v}=-3 \mathbf{i}+7 \mathbf{j}, \text { and } \mathbf{w}=-\mathbf{i}-6 \mathbf{j}$$ Find each specified vector or scalar. $$6 \mathbf{v}$$
Step-by-Step Solution
Verified Answer
The answer is \( -18 \mathbf{i} + 42 \mathbf{j} \)
1Step 1: Identify the vector \( \mathbf{v} \)
\( \mathbf{v} \) is given as \( -3 \mathbf{i} + 7 \mathbf{j} \)
2Step 2: Multiply \( \mathbf{v} \) by scalar
Multiply each component of \( \mathbf{v} \) by 6, the result is \( 6 \mathbf{v} = 6(-3 \mathbf{i} + 7 \mathbf{j}) = -18 \mathbf{i} + 42 \mathbf{j} \)
3Step 3: Formulate the result
The result of multiplying \( \mathbf{v} \) by 6 is the vector \( -18 \mathbf{i} + 42 \mathbf{j} \).
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