If 4$\widehat {\bf{i}} + 7\widehat {\bf{j}} + 8{\bf{\hat k}},\;2\widehat {\bf{i}} + 3\widehat {\bf{j}} + 4{\bf{\hat k}}$ and $2\widehat {\bf{i}} + 5\widehat {\bf{j}} + 7{\bf{\hat k}}$ are the position vectors of the vertices $A,B\;{\rm{and\;}}C$ respectively of triangle $ABC$. The position vector of the point where the bisector of angle $A$ meets $BC$ is

$\frac{1}{2}\left( {6\widehat {\bf{i}} + 13\widehat {\bf{j}} + 18{\bf{\hat k}}} \right)$

$\frac{2}{3}\left( {6\widehat {\bf{i}} + 12\widehat {\bf{j}} - 8{\bf{\hat k}}} \right)$

$\frac{1}{3}\left( { - 6\widehat {\bf{i}} - 8\widehat {\bf{j}} - 9{\bf{\hat k}}} \right)$

$\frac{2}{3}\left( { - 6\widehat {\bf{i}} - 12\widehat {\bf{j}} + 8{\bf{\hat k}}} \right)$

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JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

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Application +4 | -1

If 4

\widehat \mathbf{i} + 7\widehat \mathbf{j} + 8\mathbf{\hat k},\;2\widehat \mathbf{i} + 3\widehat \mathbf{j} + 4\mathbf{\hat k}

and

2\widehat \mathbf{i} + 5\widehat \mathbf{j} + 7\mathbf{\hat k}

are the position vectors of the vertices

A,B\;\mathrm{and\;}C

respectively of triangle

ABC

. The position vector of the point where the bisector of angle

A

meets

BC

View answer and explanation

Correct option: A

\frac{1}{2}\left( {6\widehat \mathbf{i} + 13\widehat \mathbf{j} + 18\mathbf{\hat k}} \right)

Option A (

\frac{1}{2}\left( {6\widehat \mathbf{i} + 13\widehat \mathbf{j} + 18\mathbf{\hat k}} \right)

) is correct because it represents the position vector of the point where the angle bisector of angle A intersects BC, calculated using the section formula and the angle bisector theorem.

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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