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JEE Mains · Maths · STD 12 - 10. vector algebra
If the position vectors of the vertices \(A, B\) and \(C\) of a \( \Delta ABC\) are respectively \(4\hat i + 7\hat j + 8\hat k\,,\,2\hat i + 3\hat j + 4\hat k\) and \(2\hat i + 5\hat j + 7\hat k\) then the position vector of the point, where the bisector of \(\angle A\) meets \(BC\) is
- A \(\frac{1}{2}(4\hat i + 8\hat j+ 11\hat k)\,\)
- B \(\frac{1}{3}(6\hat i + 13\hat j + 18\hat k)\,\)
- C \(\frac{1}{4}(8\hat i + 14\hat j + 9\hat k)\,\)
- D \(\frac{1}{3}(6\hat i + 11\hat j + 15\hat k)\,\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3}(6\hat i + 13\hat j + 18\hat k)\,\)
Step-by-step Solution
Detailed explanation
Let the bisector of angle \(A\) meets \(BC\) at \(D,\) then \(AD\) divides \(BC\) in the ratio \(AB: AC\) Position vectors of \(D =\) \(\frac{|\overrightarrow{A B}|(2 i+5 j+7 k)+|\overrightarrow{A C}|(2 i+3 j+4 k)}{|\overrightarrow{A B}|+|\overrightarrow{A C}|}\) Here,…
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