The vertices of a triangle are $A (1, 1, 2)$ , $B (4, 3, 1)$ and $C (2, 3, 5)$ . A vector representing the bisector of the angle A is?

^i +^j + 2^k

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2^i - 2^j +^k

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2^i + 2^j -^k

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2^i + 2^j +^k

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Solution

The correct option is A $^i +^j + 2^k$
$\begin{matrix} \frac{B D}{D C} = \frac{A B}{A C} A B = \sqrt{3^{2} + 2^{2} + 1^{2}} = \sqrt{14} A C = \sqrt{1^{2} + 2^{2} + 3^{2}} = \sqrt{14} \end{matrix}$
D is mid point of BC
A(1,1,2), D(3,3,3)
$- - \to A D = 2 ˆ i + 2 ˆ j + ˆ k$

Suggest Corrections

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\to A =^i - 2^j + 2^k, \to B = 2^i +^j -^k

\to C = 3^i -^j + 2^k

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The given vectors can form sides of a triangle $^i -^j -^k, - 2^i + 3^j -^k,^i - 2^j + 2^k$

^i + 2^j +^k

^i +^j + 2^k

2^i +^j +^k

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