If $I$ is incentre of $\Delta \;ABC,$ then $I$ is

$\frac{{a{\bf{\vec a}} + b{\bf{\vec b}} + c\;{\bf{\vec c}}}}{{a + b + c}}$

$\frac{{a{\bf{\vec a}} + b{\bf{\vec b}} + c\;{\bf{\vec c}}}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}$

$\frac{1}{3}\left[ {{\bf{\vec a}} + {\bf{\vec b}} + \;{\bf{\vec c}}} \right]$

$\frac{{{\bf{\vec a}} + {\bf{\vec b}} + {\bf{\vec c}}}}{{a + b + c}}$

Back to ADDITION OF VECTORS

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Understanding +4 | -1

I

is incentre of

\Delta \;ABC,

then

I

View answer and explanation

Correct option: A

\frac{{a\mathbf{\vec a} + b\mathbf{\vec b} + c\;\mathbf{\vec c}}}{{a + b + c}}

Option A is correct because the incenter of a triangle is a weighted average of the vertices' position vectors, with weights being the lengths of the opposite sides.

More Questions from ADDITION OF VECTORS

Practice All Chapter MCQs →

Let

\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}

and

\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}

. If

\mathbf{d}

a

unit vector such that

\mathbf{a} \cdot \mathbf{d}=0=(b \mathbf{c}

) , then

\mathbf{d}

is equal to
A vector

{\mathbf{\vec a}}

has components

2\;p

and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense, if this respect to new system

{\mathbf{\vec a}}

has components

p + 1

and 1, then If

\vec{a}, \vec{b}

and

\vec{c}

are three mutually perpendicular unit vetors and

\vec{d}

is a unit vector which makes equal angles with

\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}

ānd

\overrightarrow{\mathrm{c}}

then the value of

|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|^2

The non-zero vectors are

\vec{a}, \vec{b}

and

\vec{c}

are related by

\vec{a}=8 \vec{b}

and

\vec{c}=-7 \vec{b}

. Then the angle between

\vec{a}

and

\vec{c}

is If the vectors

2 \mathbf{i}+\mathbf{j}-\mathbf{k},-\mathbf{i}+2 \mathbf{j}+\lambda \mathbf{k}

and

-5 \mathbf{i}+2 \mathbf{j}-\mathbf{k}

ar coplanar, then the value of

\lambda

is equal The medium

AD

of the triangle

ABC

is bisected at

E,\;BE

meets

AC

F

, then

AF:AC =