If ${\rm{\vec \alpha }} + {\rm{\vec \beta }} + {\rm{\vec \gamma }} = a{\rm{\vec \delta }}\;{\rm{and}}\;{\rm{\vec \beta }} + {\rm{\vec \gamma }} + {\rm{\vec \delta }} = b{\rm{\vec \alpha }}\;{\rm{and}}\;{\rm{\vec \alpha }},{\rm{\;\vec \beta }},{\rm{\;\vec \gamma }}$ are non-coplanar and ${{\rm{\vec \alpha }}}$ is not parallel to ${{\rm{\vec \delta }}}$, then ${\rm{\vec \alpha }} + {\rm{\vec \beta }} + {\rm{\vec \gamma }}$ $ + {\rm{\vec \delta }}$ equals

$\left( {a + b} \right){\rm{\vec \gamma }}$

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Analyzing +4 | -1

\mathrm{\vec \alpha } + \mathrm{\vec \beta } + \mathrm{\vec \gamma } = a\mathrm{\vec \delta }\;\mathrm{and}\;\mathrm{\vec \beta } + \mathrm{\vec \gamma } + \mathrm{\vec \delta } = b\mathrm{\vec \alpha }\;\mathrm{and}\;\mathrm{\vec \alpha },\mathrm{\;\vec \beta },\mathrm{\;\vec \gamma }

are non-coplanar and

{\mathrm{\vec \alpha }}

is not parallel to

{\mathrm{\vec \delta }}

, then

\mathrm{\vec \alpha } + \mathrm{\vec \beta } + \mathrm{\vec \gamma }

+ \mathrm{\vec \delta }

equals

View answer and explanation

Correct option: C

The correct answer is C (0) because, given the conditions and the non-coplanar nature of the vectors, the sum of all vectors must equal zero.

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 =