If \( \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}} \) bisects the angle between a and \(...
If \( \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}} \) bisects the angle between a and \( -\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}} \), where \( \mathbf{a} \) is a unit vector, then
(a) \( \mathrm{a}=\frac{1}{105}(41 \hat{\mathbf{i}}+88 \hat{\mathbf{j}}-40 \hat{\mathbf{k}}) \)
(b) \( \mathrm{a}=\frac{1}{105}(41 \hat{\mathbf{i}}+88 \hat{\mathrm{j}}+40 \hat{\mathrm{k}}) \)
(c) \( \mathbf{a}=\frac{1}{105}(-41 \hat{\mathrm{i}}+88 \hat{\mathbf{j}}-40 \hat{\mathrm{k}}) \)
(d) \( \mathrm{a}=\frac{1}{105}(41 \hat{\mathbf{i}}-88 \hat{\mathrm{j}}-40 \hat{\mathrm{k}}) \)
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