If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are position vectors of the vertices of $\triangle A B C$, then…

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are position vectors of the vertices of $\triangle A B C$, then $\frac{(\mathbf{a}-\mathbf{c}) \times(\mathbf{b}-\mathbf{a})}{(\mathbf{b}-\mathbf{a}) \cdot(\mathbf{c}-\mathbf{a})}=$
  1. $\cot C$
  2. $\tan A$
  3. $\tan C$
  4. $-\tan A$

Solution

$ \text { } \frac{(\mathbf{a}-\mathbf{c}) \times(\mathbf{b}-\mathbf{a})}{(\mathbf{b}-\mathbf{a}) \cdot(\mathbf{c}-\mathbf{a})}=\frac{\mathbf{C A} \times \mathbf{A B}}{\mathbf{A B} \cdot \mathbf{A C}} $
Hence, option (2) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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