True False[1 Marks ]

Question 11 Mark

State True or False for the following:
The formula $(\vec{\text{a}}+\vec{\text{b}})=\vec{\text{a}}^2+\vec{\text{b}}^2+2\vec{\text{a}}\times\vec{\text{b}}$ is valid for non-zero vectors $\vec{\text{a}}$ and $\vec{\text{b}}.$

Answer

False.Solution:
$(\vec{\text{a}}+\vec{\text{b}})=(\vec{\text{a}}+\vec{\text{b}})\cdot(\vec{\text{a}}+\vec{\text{b}})$
$(\vec{\text{a}}+\vec{\text{b}})=\vec{\text{a}}^2+\vec{\text{b}}^2+2\vec{\text{a}}\cdot\vec{\text{b}}$

View full question & answer→

Question 21 Mark

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.

View full question & answer→

Question 31 Mark

Two vectors having same magnitude are collinear.

Answer

False, Collinear vectors may not have a same magnitude.

View full question & answer→

Question 41 Mark

State True or False for the following:
Position vector of a point $\vec{\text{P}}$ is a vector whose initial point is origin.

Answer

True.Solution:
Since, $\vec{\text{P}}=\overrightarrow{\text{OP}}$ displacement of vector $\vec{\text{P}}$ from origin.

View full question & answer→

Question 51 Mark

State True or False for the following:
If $|\vec{\text{a}}+\vec{\text{b}}|=|\vec{\text{a}}-\vec{\text{b}}|,$ then the vector $\vec{\text{a}}$ and $\vec{\text{b}}$ are orthogonal.

Answer

True.Solution:
Given, $|\vec{\text{a}}+\vec{\text{b}}|=|\vec{\text{a}}-\vec{\text{b}}|$
$\Rightarrow|\vec{\text{a}}+\vec{\text{b}}|^2=|\vec{\text{a}}-\vec{\text{b}}|^2$
$\Rightarrow|\vec{\text{a}}|^2+|\vec{\text{b}}|^2+2\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}|^2+|\vec{\text{b}}|^2-2\vec{\text{a}}\cdot\vec{\text{b}}$
$\Rightarrow2\vec{\text{a}}\cdot\vec{\text{b}}=-2\vec{\text{a}}\cdot\vec{\text{b}}$
$\Rightarrow4\vec{\text{a}}\cdot\vec{\text{b}}=0$
$\Rightarrow\vec{\text{a}}\cdot\vec{\text{b}}=0$
Hence, $\vec{\text{a}}$ and $\vec{\text{b}}$ are orthogonal.

View full question & answer→

Question 61 Mark

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

False.Solution:
If $\vec{\text{a}}\cdot{\text{b}}=0,$ then $\vec{\text{a}}$ and ${\text{b}}$ are perpendicular to each other.
In rhombus, adjacent sides are not necessarily perpendicular.

View full question & answer→

Question 71 Mark

Zero vector is unique.

Answer

False.

View full question & answer→

Question 81 Mark

Two collinear vectors having the same magnitude are equal.

Answer

False, As two collinear vectors are equal only if they have same length and same sense.

View full question & answer→

Question 91 Mark

Answer the following as true or false.
Two collinear vectors are always equal in magnitude.

Answer

False $[\because\ \vec{a}\ \ \text{and}\ 2\vec{a}$ are collinear vectors but $ \Big|2\vec{a}\Big|=2\Big|\vec{a}\Big|]$

View full question & answer→

Question 101 Mark

Answer the following as true or false.
$\vec{a} \ \text{and}\ -\vec{a}$ are collinear.

Answer

True.

View full question & answer→

Question 111 Mark

Answer the following as true or false.
Two collinear vectors having the same magnitude are equal.

Answer

False $[\because$ Vectors $\vec{a}\ \text{and}-\vec{a}\left\{=(-1) \vec{a}=\vec{ma}\right\}$ are collinear vectors and $\Big|\vec{a}\Big|=\Big|-\vec{a}\Big|$ but we know that $\vec{a}\neq-\vec{a}$ because their directions are opposite.]

View full question & answer→

Question 121 Mark

Answer the following as true or false.
Two vectors having same magnitude are collinear.

Answer

False $[\because\ \Big|\hat{i}\Big|=\Big|\hat{j}\Big|=1$ bat $\hat{i}\ \text{and}\ \vec{j}$ are vectors along x - axis (OX) and y - axis (OY) respectively]

View full question & answer→

Question 131 Mark

Answer the following as true or false:
$\vec{\text{a}}\text{ and }\vec{\text{a}}$ are collinear.

Answer

True, As vectors having the same and parallel support are collinear.

View full question & answer→

Question 141 Mark

Two collinear vectors are always equal in magnitude.

Answer

False, Collinear vectors are parallel vector not equal vectors.

View full question & answer→

MATHS True False[1 Marks ]

Test yourself on this topic