If $P,\;Q,\;R$ are the mid-points of the sides $AB,\;BC$ and $CA$ of ${\rm{\Delta }}ABC$ are $O$ is a point within the triangle, then $\vec OA + \vec OB + \vec OC = $

$2\left( {\vec OP + \vec OQ + \vec OR} \right)$

$4\left( {\vec OP + \vec OQ + \vec OR} \right)$

$6\left( {\vec OP + \vec OQ + \vec OR} \right)$

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Understanding +4 | -1

P,\;Q,\;R

are the mid-points of the sides

AB,\;BC

and

CA

\mathrm{\Delta }ABC

are

O

is a point within the triangle, then

\vec OA + \vec OB + \vec OC =

View answer and explanation

Correct option: B

\vec OP + \vec OQ + \vec OR

Option B (

\vec OP + \vec OQ + \vec OR

) is correct because it directly follows from expressing

\vec OA + \vec OB + \vec OC

in terms of the midpoints P, Q, and R.

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\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 =