The vector sum of two forces vec{A} and vec{B | vedclass

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

Question

(D) Let the two forces be $\vec{A}$ and $\vec{B}$.The vector sum is $(\vec{A} + \vec{B})$ and the vector difference is $(\vec{A} - \vec{B})$.Given tha

Vedclass · Accepted Answer

equal in magnitude.

Vedclass · Answer

(D) Let the two forces be $\vec{A}$ and $\vec{B}$.The vector sum is $(\vec{A} + \vec{B})$ and the vector difference is $(\vec{A} - \vec{B})$.Given that the sum is perpendicular to the difference,their dot product must be zero:$(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$Expanding the dot product:$\vec{A} \cdot \vec{A} - \vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{A} - \vec{B} \cdot \vec{B} = 0$Since the dot product is commutative,$\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$,so the terms cancel out:$|\vec{A}|^2 - |\vec{B}|^2 = 0$$|\vec{A}|^2 = |\vec{B}|^2$$|\vec{A}| = |\vec{B}|$Therefore,the forces are equal in magnitude.

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence,the forces $\vec{A}$ and $\vec{B}$ are

Similar Questions

$A$ vector is added to an equal and opposite vector of similar nature,it forms a ........

Find the unit vector in the direction of $2\hat{i} + 3\hat{j} + 4\hat{k}$.

If $\overrightarrow A = 2\hat i + 4\hat j - 5\hat k$,the direction cosines of the vector $\overrightarrow A$ are:

A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius $r$ with time $t$ is ... (where $k$ is a positive constant)

$\vec{A}$ is a vector of magnitude $2.7$ units due east. What is the magnitude and direction of vector $4 \vec{A}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module