Find |Delta overrightarrow{a}| and Delta a wh | vedclass

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

Question

(B) Let the initial vector be $\overrightarrow{OA}$ and the final vector after rotation be $\overrightarrow{OB}$.Given that the magnitude of the vecto

Vedclass · Accepted Answer

$a\,d	heta, 0$

Vedclass · Answer

(B) Let the initial vector be $\overrightarrow{OA}$ and the final vector after rotation be $\overrightarrow{OB}$.Given that the magnitude of the vector remains constant,$|\overrightarrow{OA}| = |\overrightarrow{OB}| = a$.The change in the vector is defined as $\Delta \overrightarrow{a} = \overrightarrow{OB} - \overrightarrow{OA}$.From the geometry of the triangle $OAB$,the magnitude of the change in the vector is the length of the chord $AB$.For a small angle $d	heta$,the arc length $AB$ is given by $AB = a \cdot d	heta$.Therefore,$|\Delta \overrightarrow{a}| = a \cdot d	heta$.Now,consider the change in the magnitude of the vector,$\Delta a = |\overrightarrow{OB}| - |\overrightarrow{OA}|$.Since the magnitude is constant,$\Delta a = a - a = 0$.Thus,$|\Delta \overrightarrow{a}| = a \cdot d	heta$ and $\Delta a = 0$.

Find $|\Delta \overrightarrow{a}|$ and $\Delta a$ when a vector $\overrightarrow{a}$ is rotated by an angle $d\theta$.

Similar Questions

The position vectors of points $A, B, C$ and $D$ are $A = 3\hat{i} + 4\hat{j} + 5\hat{k}$,$B = 4\hat{i} + 5\hat{j} + 6\hat{k}$,$C = 7\hat{i} + 9\hat{j} + 3\hat{k}$ and $D = 4\hat{i} + 6\hat{j}$. Then the displacement vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are:

What is a vector? How can it be represented?

$A$ vector has a magnitude the same as that of $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\overrightarrow{B} = 4 \hat{i} + 3 \hat{j}$. The $x$ and $y$ components of this vector in the first quadrant are $X$ and $3$ respectively,where $X = $ . . . . . . .

$0.4\hat i + 0.8\hat j + c\hat k$ represents a unit vector when $c$ is

If $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$,then the angle between vector $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module