If ${\bf{\vec a}} = \widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}},\;{\bf{\vec b}} = \widehat {\bf{i}} - \widehat {\bf{j}} + 2{\bf{\hat k}}$ and ${\bf{\vec c}} = x\;\widehat {\bf{i}} + \left( {x - 2} \right)\widehat {\bf{j}} - {\bf{\hat k}}$ and if the vector ${{\bf{\vec c}}}$ lies in the plane of vectors ${{\bf{\vec a}}}$ and ${\bf{\vec b}},$ then $x$ equals

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Application +4 | -1

\mathbf{\vec a} = \widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k},\;\mathbf{\vec b} = \widehat \mathbf{i} - \widehat \mathbf{j} + 2\mathbf{\hat k}

and

\mathbf{\vec c} = x\;\widehat \mathbf{i} + \left( {x - 2} \right)\widehat \mathbf{j} - \mathbf{\hat k}

and if the vector

{\mathbf{\vec c}}

lies in the plane of vectors

{\mathbf{\vec a}}

and

\mathbf{\vec b},

then

x

equals

View answer and explanation

Correct option: C

- 2

Option C (-2) is correct because if

\mathbf{\vec c}

lies in the plane of

\mathbf{\vec a}

and

\mathbf{\vec b}

, then

\mathbf{\vec a}

\mathbf{\vec b}

, and

\mathbf{\vec c}

are coplanar, and their scalar triple product is zero, leading to x = -2.

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 =