If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=3…

If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\), then find the angle between the vectors \(2 \mathbf{a}+\mathbf{b}\) and \(\mathbf{a}+2 \mathbf{b}\).
  1. \(\cos ^{-1}\left(\frac{36}{\sqrt{42 \times 35}}\right)\)
  2. \(\cos ^{-1}\left(\frac{72}{\sqrt{24 \times 32}}\right)\)
  3. \(\cos ^{-1}\left(\frac{52}{\sqrt{74 \times 65}}\right)\)
  4. \(\cos ^{-1}\left(\frac{24}{\sqrt{18 \times 32}}\right)\)

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

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