First slide

Scalars and Vectors

Question

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

Moderate

A

are equal to each other in magnitude
B

are not equal to each other in magnitude
C

cannot be predicted
D

are equal to each other

Solution

If two vectors are perpendicular then their dot product must be equal to zero.
Let say two vectors are $\vec{A}$ and $\vec{B}$ . According to problem $(\vec{A} + \vec{B})$ is perpendicular to $(\vec{A} - \vec{B})$ .
$\begin{array}{l} \begin{array}{l} ∴ (\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0 \\ \Rightarrow \vec{A} \cdot \vec{A} - \vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{A} - \vec{B} \cdot \vec{B} = 0 \end{array} \\ \begin{array}{l} \Rightarrow A^{2} - B^{2} = 0 \\ \Rightarrow A^{2} = B^{2} \end{array} \end{array}$
$∴$ A = B i.e., two vectors are equal to each other in magnitude.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App