If a vector `\vec {B}` is added to vector  `\vec {A}`, the result is 6`\hat {i}` + `\hat {j}` . If  `\vec {B}` is subtracted from  `\vec {A}`, the result is -4 `\hat {i}` + 7`\hat {j}` . What is the magnitude of vector `\vec {A}`?⃗⃖

(Ans: 4.1)


Given:

`\vec {A}` + `\vec {B}` = 6`\hat {i}` + `\hat {j}` 
`\vec {A}` - `\vec {B}` = -4`\hat {i}` + 7`\hat {j}`


To Find:

Magnitude of the Vector = |`\vec {A}`| = ?


Solution: 

By adding the given two equations we get

`\vec {A}` + `\vec {B}` = 6`\hat {i}` + `\hat {j}` 
`\vec {A}` - `\vec {B}` = -4`\hat {i}` + 7`\hat {j}`
________________________________________________
2`\vec {A}`     = 2`\hat {i}` + 8`\hat {j}`

or (dividing both sides by 2)

`\vec {A}`  = `\hat {i}` + 4`\hat {j}`

Here x-component = 1 and y-component = 4 . So, to find its magnitude |`\vec {A}`| we have

|`\vec {A}`| = `\sqrt {x^2 + y^2}`

by putting values 

A = `\sqrt {(1)^2 + (4)^2}`

A = `\sqrt {1 + 16}`

A = `\sqrt {17}`

A = 4.1    --------Ans

Thus the magnitude of the vector `\vec {A}` is 4.1


************************************
************************************
Numerical Problem 2.5
⇑
List of 11th Physics Numerical Problems of Chapter - 2
⇑



************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.