(C) $I$: Two vectors $\vec{a}$ and $\vec{b}$ are linearly independent if and only if they are non-zero and non-collinear. Thus,statement $I$ is true.$

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) $I$: Two vectors $\vec{a}$ and $\vec{b}$ are linearly independent if and only if they are non-zero and non-collinear. Thus,statement $I$ is true.$II$: Any three coplanar vectors in a $3D$ space are linearly dependent because one can be expressed as a linear combination of the other two if they are not collinear,or they are linearly dependent if any two are collinear. Thus,statement $II$ is true.$\therefore$ Both $I$ and $II$ are true.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

Easy

$I$. Two non-zero,non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

TS EAMCET 2005 All TS EAMCET

AP EAMCET 2005 All AP EAMCET

A
Only $I$
B
Only $II$
C
Both $I$ and $II$
D
Neither $I$ nor $II$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Vector Algebra

Subtopic

Basic , Modulus and Algebra of vectors

Previous Year

TS EAMCET 2005 Paper All TS EAMCET years →

Previous Year

AP EAMCET 2005 Paper All AP EAMCET years →

If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar,then $\lambda \vec{a}$ is a unit vector if

Easy

View Solution

$ABCDEF$ is a regular hexagon whose centre is $O$. Then,$\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF}$ is equal to (in $vec{AO}$)

EasyTS EAMCET 2016

View Solution

Find a vector of magnitude $5$ units,and parallel to the resultant of the vectors $\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}.$

Medium

View Solution

In the given figure (a square),identify the following vectors:
Equal vectors.

Medium

View Solution

If $P$ and $Q$ are the midpoints of the sides $BC$ and $CD$ of the parallelogram $ABCD$,then $\overrightarrow{AP} + \overrightarrow{AQ} = $

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$I$. Two non-zero,non-collinear vectors are linearly independent.$II$. Any three coplanar vectors are linearly dependent.Which of the above statements is/are true?

Similar Questions

If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar,then $\lambda \vec{a}$ is a unit vector if

$ABCDEF$ is a regular hexagon whose centre is $O$. Then,$\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF}$ is equal to (in $vec{AO}$)

Find a vector of magnitude $5$ units,and parallel to the resultant of the vectors $\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}.$

In the given figure (a square),identify the following vectors:Equal vectors.

If $P$ and $Q$ are the midpoints of the sides $BC$ and $CD$ of the parallelogram $ABCD$,then $\overrightarrow{AP} + \overrightarrow{AQ} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$I$. Two non-zero,non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

In the given figure (a square),identify the following vectors:
Equal vectors.