The resultant of two vectors vec{A} and vec{B | vedclass

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

Question

(C) Let the vectors be $\vec{A}$ and $\vec{B}$. The resultant is $\vec{C} = \vec{A} + \vec{B}$.Taking the dot product of $\vec{C}$ with itself,we get

Vedclass · Accepted Answer

$B$

Vedclass · Answer

(C) Let the vectors be $\vec{A}$ and $\vec{B}$. The resultant is $\vec{C} = \vec{A} + \vec{B}$.Taking the dot product of $\vec{C}$ with itself,we get $C^2 = A^2 + B^2 + 2\vec{A} \cdot \vec{B}$.When the magnitude of $\vec{B}$ is doubled,the new resultant is $\vec{C}' = \vec{A} + 2\vec{B}$.It is given that $\vec{C}'$ is perpendicular to $\vec{A}$,so $\vec{A} \cdot \vec{C}' = 0$.$\vec{A} \cdot (\vec{A} + 2\vec{B}) = 0 \implies A^2 + 2\vec{A} \cdot \vec{B} = 0$.This implies $2\vec{A} \cdot \vec{B} = -A^2$.Substituting this into the expression for $C^2$:$C^2 = A^2 + B^2 - A^2 = B^2$.Therefore,the magnitude of $\vec{C}$ is $B$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled,the new resultant vector becomes perpendicular to $\vec{A}$. Then the magnitude of $\vec{C}$ is

Similar Questions

Among three vectors,two vectors are equal in magnitude,and the magnitude of the third vector is $\sqrt{2}$ times the magnitude of the other two vectors. If $\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = 0$,find the angles between the vectors.

The magnitudes of two vectors are $A$ and $B$ $(A > B)$. If the maximum resultant magnitude of the two vectors is $n$ times their minimum resultant magnitude,then $\frac{A}{B} =$

Two vectors of equal magnitude $5$ units have an angle $60^\circ$ between them. Find the magnitude of $(a)$ the sum of the vectors and $(b)$ the difference of the vectors.

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

The sum of the magnitudes of two forces is $25 \,N$. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $10 \,N$. The two forces are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module