Let ${\bf{\vec a}}\;,{\bf{\vec b}},,\overrightarrow {{\bf{c}}\;} \;\;$ be three non-zero vectors such that no two of these are collinear. If the vector ${\bf{\vec a}} + 2\;{\bf{\vec b}}$ is collinear with $\overrightarrow {{\bf{c}}\;} \;,$ then $\overrightarrow {{\bf{a}}\;} + 2\overrightarrow {{\bf{b}}\;} + 6\;\overrightarrow {{\bf{c}}\;} \;\;{\rm{equals}}\;\;\;$

$\lambda \;{\bf{\vec c}}\;\left( {\lambda \ne 0,\;{\rm{a\;scalar}}} \right)$

$\lambda \;{\bf{\vec a}}\;\left( {\lambda \ne 0,\;{\rm{a\;scalar}}} \right)$

$\lambda \;{\bf{\vec b}}\;\left( {\lambda \ne 0,\;{\rm{a\;scalar}}} \right)$

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Application +4 | -1

Let

\mathbf{\vec a}\;,\mathbf{\vec b},,\overrightarrow {\mathbf{c}\;} \;\;

be three non-zero vectors such that no two of these are collinear. If the vector

\mathbf{\vec a} + 2\;\mathbf{\vec b}

is collinear with

\overrightarrow {\mathbf{c}\;} \;,

then

\overrightarrow {\mathbf{a}\;} + 2\overrightarrow {\mathbf{b}\;} + 6\;\overrightarrow {\mathbf{c}\;} \;\;\mathrm{equals}\;\;\;

View answer and explanation

Correct option: C

\lambda \;\mathbf{\vec c}\;\left( {\lambda \ne 0,\;\mathrm{a\;scalar}} \right)

Option C (

\lambda \;\mathbf{\vec c}\;(\lambda \ne 0,\;\mathrm{a\;scalar}))

is correct because

\mathbf{\vec a} + 2\mathbf{\vec b}

is a scalar multiple of

\mathbf{\vec c}

, and adding

6\mathbf{\vec c}

results in another scalar multiple of

\mathbf{\vec c}