$A,B,C,D,E,F\;$ in that order, are the vertices of a regular hexagon with center origin. If the position vectors $A\;$ and $B$ are respectively, $4\;\widehat {\bf{i}} + 3\widehat {\bf{j}} - {\bf{\hat k}}$ and $ - 3\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}},$ then $\overrightarrow {{\bf{DE}}} $ is equal to

$7\widehat {\bf{i}} + 2\widehat {\bf{j}} - 2{\bf{\hat k}}$

$ - 7\widehat {\bf{i}} - 2\widehat {\bf{j}} + 2{\bf{\hat k}}$

$3\widehat {\bf{i}} - \widehat {\bf{j}} - {\bf{\hat k}}$

$ - 4\widehat {\bf{i}} - 3\widehat {\bf{j}} + 2{\bf{\hat k}}$

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JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Application +4 | -1

A,B,C,D,E,F\;

in that order, are the vertices of a regular hexagon with center origin. If the position vectors

A\;

and

B

are respectively,

4\;\widehat \mathbf{i} + 3\widehat \mathbf{j} - \mathbf{\hat k}

and

- 3\widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k},

then

\overrightarrow {\mathbf{DE}}

is equal to

View answer and explanation

Correct option: A

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

The correct answer is A. In a regular hexagon with center at the origin,

\overrightarrow {\mathbf{DE}}

is equal to

- \overrightarrow {\mathbf{AB}}

, which can be calculated from the given position vectors.

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 =