Problem 30 - Algebra and Trigonometry

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. $$-7 \mathbf{w}$$

Step-by-Step Solution

Answer

The product obtained after scaling vector \(\mathbf{w}\) by -7 is \(7\mathbf{i}+42\mathbf{j}\).

Step 1: Identify the Vector

Identify vector \(\mathbf{w}\) which is given as \(-\mathbf{i}-6\mathbf{j}\).

Step 2: Multiply the Scalar and the Vector

Multiply the scalar -7 with each component of vector \(\mathbf{w}\) to find \(-7 \mathbf{w}\). This operation gives \(-7(-\mathbf{i}-6\mathbf{j}) = 7\mathbf{i}+42\mathbf{j}\).