Problem

Given two vectors \(\mathbf{A} = 3\mathbf{i} + 2\mathbf{j}\) and \(\mathbf{B} = \mathbf{i} + 4\mathbf{j}\), find the position vector \(\mathbf{R}\) such that \(\mathbf{R} = 2\mathbf{A} - \mathbf{B}\).

Answer

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Answer

Secondly, subtract \(\mathbf{B}\) from \(2\mathbf{A}\) to get \(\mathbf{R} = 2\mathbf{A} - \mathbf{B} = (6\mathbf{i} + 4\mathbf{j}) - (\mathbf{i} + 4\mathbf{j}) = 5\mathbf{i}\).

Steps

Step 1 ：Firstly, find the vector \(2\mathbf{A} = 2(3\mathbf{i} + 2\mathbf{j}) = 6\mathbf{i} + 4\mathbf{j}\).

Step 2 ：Secondly, subtract \(\mathbf{B}\) from \(2\mathbf{A}\) to get \(\mathbf{R} = 2\mathbf{A} - \mathbf{B} = (6\mathbf{i} + 4\mathbf{j}) - (\mathbf{i} + 4\mathbf{j}) = 5\mathbf{i}\).

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