Download App

VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA1 Mark
Question
State True or False for the following:
If $|\vec{\text{a}}|=|\vec{\text{b}}|,$ then necessarily it implies $\vec{\text{a}}=\pm\vec{\text{b}}.$
✓

Answer

False.Solution:
Consider $\vec{\text{a}}=2\hat{\text{i}}+2\hat{\text{j}}-2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}}$
Clearly $|\vec{\text{a}}|=|\vec{\text{b}}|,$ but $\vec{\text{a}}=\pm\vec{\text{b}}$
So, the given statement false.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from VECTOR ALGEBRA→VECTOR ALGEBRA — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

State True or False for the following:
Solution of the differential equation of the type $\frac{\text{dy}}{\text{dx}}+\text{P}_1\text{x}=\text{Q}_1$ is given by $\text{x.I.F.}=\int(\text{I.F.})\times\text{Q}_1\text{dy}.$
→
State True or False for the statements:
The composition of two continuous function is a continuous function.
→
State True or False for the statements:
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.
→
State True or False for the statements:
If A and B′ are independent events, then $\text{P}(\text{A}'\cup\text{B})=1-\text{P}(\text{A})\text{P}(\text{B'}).$
→
State True or False for the following:
The solution of $\frac{\text{dy}}{\text{dx}}=\Big(\frac{\text{y}}{\text{x}}\Big)^{\frac{1}{3}}$ is $\text{y}^{\frac{2}{3}}-\text{x}^{\frac{2}{3}}=\text{C}.$
→
State True or False for the following:
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are adjacent sides of a rhombus, then $\vec{\text{a}}\cdot{\text{b}}=0.$
→
Answer the following as true or false:
$\vec{\text{a}}\text{ and }\vec{\text{a}}$ are collinear.
→
State True or False for the statements of the following Exercise:
The determinant $\begin{vmatrix}\sin\text{A}&\cos\text{A}&\sin\text{A}+\cos\text{B}\\\sin\text{B}&\cos\text{A}&\sin\text{B}+\cos\text{B}\\\sin\text{C}&\cos\text{A}&\sin\text{C}+\cos\text{B}\end{vmatrix}$ is equal to zero.
→
Answer the following as true or false:
$\vec{\text{a}}\text{ and }\vec{\text{a}}$ are collinear.
→
State True or False for the statements.
The relation R on the set A = {1, 2, 3} defined as R = {(1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.
→