$D,\;E$ and $F$ are the mid-points of the sides $BC,\;CA$ and $AB$ respectively of ${\rm{\Delta }}ABC$ and $G$ is the centroid of the triangle, then $\overrightarrow {GD} + \overrightarrow {GE} + \overrightarrow {GF} = $

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

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D,\;E

and

F

are the mid-points of the sides

BC,\;CA

and

AB

respectively of

\mathrm{\Delta }ABC

and

G

is the centroid of the triangle, then

\overrightarrow {GD} + \overrightarrow {GE} + \overrightarrow {GF} =

View answer and explanation

Correct option: A

{\vec 0}

Option A (

\vec 0

) is correct because the sum of the vectors from the centroid to the midpoints of the sides of a triangle is always the zero vector.

Practice All Chapter MCQs →

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

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

\mathbf{d}

a

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

\mathbf{d}

{\mathbf{\vec a}}

2\;p

{\mathbf{\vec a}}

p + 1

\vec{a}, \vec{b}

\vec{c}

\vec{d}

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

\overrightarrow{\mathrm{c}}

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

\vec{a}, \vec{b}

\vec{c}

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

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

\vec{a}

\vec{c}

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

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

\lambda

AD

ABC

E,\;BE

AC

F

AF:AC =