CBSE (Commerce) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for If the Sum of Two Unit Vectors is a Unit Vector Prove that the Magnitude of Their Difference is √ 3 . - CBSE (Commerce) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is \[\sqrt{3}\].

Solution

\[\text{ Given that } \hat{a}\ , \hat{b}\ \text{ and }\left| \hat{a} + \hat{b} \right|\text{ are unit vectors }.\]
\[So,\left| \hat{a} \right|=1,\left| \hat{b} \right|=1 and\left| \left| \hat{a} + \hat{b} \right| \right|=1\]
\[\text{ We have }\]
\[ \left| \hat{a} + \hat{b} \right|^2 + \left| \hat{a} - \hat{b} \right|^2 = 2\left( \left| \hat{a} \right|^2 + \left| \hat{b} \right|^2 \right)\]
\[ \Rightarrow 1 + \left| \hat{a} - \hat{b} \right|^2 = 2\left( 1 + 1 \right)\]
\[ \Rightarrow 1 + \left| \hat{a} - \hat{b} \right|^2 = 4\]
\[ \Rightarrow \left| \hat{a} - \hat{b} \right|^2 = 3\]
\[ \Rightarrow \left| \hat{a} - \hat{b} \right| = \sqrt{3}\]

  Is there an error in this question or solution?
Solution If the Sum of Two Unit Vectors is a Unit Vector Prove that the Magnitude of Their Difference is √ 3 . Concept: Basic Concepts of Vector Algebra.
S
View in app×