The vector c , directed along the internal bisector of the angle between the vectors, a…
Mathematics · JEE Main · NTA Exams — Three Dimensional Geometry
The vector \(\stackrel{\rightharpoonup}{\mathrm{c}}\), directed along the internal bisector of the angle between the vectors, \(\overrightarrow{\mathrm{a}}=7 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) with \(|\overrightarrow{\mathrm{c}}|=5 \sqrt{6}\) is :
- \(\frac{5}{3}(\hat{\mathrm{i}}-7 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
- \(\frac{5}{3}(5 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
- \(\frac{5}{3}(\hat{\mathrm{i}}+7 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
- \(\frac{5}{3}(-5 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Answer
(A) 5 3 ( i -7 j +2 k )
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