Let ${{\bf{\vec a}}}$ and ${{\bf{\vec b}}}$ are non-collinear vectors. If there exists scalars ${\rm{\alpha }},{\rm{\beta }}$ such that ${\rm{\alpha }}{\bf{\vec a}} + {\rm{\beta }}{\bf{\vec b}} = \vec 0$, then

${\rm{\alpha }} = {\rm{\beta }} = 0$

${\rm{\alpha }} = {\rm{\beta }} \ne 0$

${\rm{\alpha }} + {\rm{\beta }} = 0$

${\rm{\alpha }} \ne {\rm{\beta }}$

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JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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Understanding +4 | -1

Let

{\mathbf{\vec a}}

and

{\mathbf{\vec b}}

are non-collinear vectors. If there exists scalars

\mathrm{\alpha },\mathrm{\beta }

such that

\mathrm{\alpha }\mathbf{\vec a} + \mathrm{\beta }\mathbf{\vec b} = \vec 0

, then

View answer and explanation

Correct option: C

\mathrm{\alpha } = \mathrm{\beta } = 0

Option C (

\mathrm{\alpha } = \mathrm{\beta } = 0

) is correct because for non-collinear vectors, the only way for the linear combination to be zero is if both scalars are zero.

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 =