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Problem If a = i ^ + j ^ + k ^ \mathbf{a} = \hat{\mathbf{i}} + \hat{\mathbf{j}} + \hat{\mathbf{k}} a = i ^ + j ^ + k ^ b = i ^ − j ^ \mathbf{b} = \hat{\mathbf{i}} - \hat{\mathbf{j}} b = i ^ − j ^ ( a ⋅ i ^ ) i ^ + ( a ⋅ j ^ ) j ^ + ( a ⋅ k ^ ) k ^ (\mathbf{a} \cdot \hat{\mathbf{i}})\hat{\mathbf{i}} + (\mathbf{a} \cdot \hat{\mathbf{j}})\hat{\mathbf{j}} + (\mathbf{a} \cdot \hat{\mathbf{k}})\hat{\mathbf{k}} ( a ⋅ i ^ ) i ^ + ( a ⋅ j ^ ) j ^ + ( a ⋅ k ^ ) k ^ ( b ⋅ i ^ ) i ^ + ( b ⋅ j ^ ) j ^ + ( b ⋅ k ^ ) k ^ (\mathbf{b} \cdot \hat{\mathbf{i}})\hat{\mathbf{i}} + (\mathbf{b} \cdot \hat{\mathbf{j}})\hat{\mathbf{j}} + (\mathbf{b} \cdot \hat{\mathbf{k}})\hat{\mathbf{k}} ( b ⋅ i ^ ) i ^ + ( b ⋅ j ^ ) j ^ + ( b ⋅ k ^ ) k ^ i ^ + j ^ − 2 k ^ \hat{\mathbf{i}} + \hat{\mathbf{j}} - 2\hat{\mathbf{k}} i ^ + j ^ − 2 k ^ Browse the problem library