If the position vectors of the vertices A, B and C of a ΔABC are respectively. 4i¯+7j¯+8k¯, 2i¯+3j¯+4k¯ and 2i¯+5j¯+7k¯, then the position vector of the point, where the bisector ∠A meets BC is

A(4,7,8), B(2,3,4), C(2,5,7)D Divides BC in AB :AC=6:6=2:1D(2(2)+1(2)2+1,2(5)+1(3)2+1,2(7)+1(4)2+1)⇒OD¯=13(6i¯+13j¯+18k¯)

If the position vectors of the vertices A, B and C of a ΔABC are respectively. 4i¯+7j¯+8k¯, 2i¯+3j¯+4k¯ and 2i¯+5j¯+7k¯, then the position vector of the point, where the bisector ∠A meets BC is

A(4,7,8), B(2,3,4), C(2,5,7)D Divides BC in AB :AC=6:6=2:1D(2(2)+1(2)2+1,2(5)+1(3)2+1,2(7)+1(4)2+1)⇒OD¯=13(6i¯+13j¯+18k¯)

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If the position vectors of the vertices A, B and C of a $Δ A B C$ are respectively. $4 \bar{i} + 7 \bar{j} + 8 \bar{k}, 2 \bar{i} + 3 \bar{j} + 4 \bar{k}$ and $2 \bar{i} + 5 \bar{j} + 7 \bar{k}$ , then the position vector of the point, where the bisector $∠ A$ meets BC is

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$\frac{1}{3} (6 i + 11 \bar{j} + 15 \bar{k})$

$\frac{1}{3} (6 \bar{i} + 13 \bar{j} + 18 \bar{k})$

$\frac{1}{4} (8 \bar{i} + 14 \bar{j} + 19 \bar{k})$

$\frac{1}{2} (4 \bar{i} + 8 \bar{j} + 11 \bar{k})$

answer is B.

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Detailed Solution

$\begin{array}{l} A (4, 7, 8), B (2, 3, 4), C (2, 5, 7) \\ D D i v i d e s B C i n A B : A C = 6 : 6 = 2 : 1 \\ D (\frac{2 (2) + 1 (2)}{2 + 1}, \frac{2 (5) + 1 (3)}{2 + 1}, \frac{2 (7) + 1 (4)}{2 + 1}) \\ \Rightarrow \bar{O D} = \frac{1}{3} (6 \bar{i} + 13 \bar{j} + 18 \bar{k}) \end{array}$