Find the magnitude and direction of vectors represented by the following pair of components
(a)  →Ax −→Ax = - 2.3 cm,  →Ay −→Ay = + 4.1 cm (b)  →Ax −→Ax = +3.9 cm,  →Ay −→Ay = -1.8 cm 
(Ans. (a) A= 4.7 and θ = 119.3°, (b) A = 4.3 and θ = 335.2°)

Given:

(a)  →Ax −→Ax = - 2.3 cm,  →Ay −→Ay = + 4.1 cm 
(b)  →Ax −→Ax = +3.9 cm,  →Ay −→Ay = -1.8 cm  

To Find:

(a) 
Magnitude of vector  →A →A = A = ?
Direction (angle θ) = ?

(b) 
Magnitude of vector  →A →A = A = ?
Direction (angle θ) = ?

Solution:

(a)  →Ax −→Ax = - 2.3 cm,  →Ay −→Ay = + 4.1 cm 


The formula to find the magnitude of vector A from its x and y component is 

A  = √Ax2+Ay2√Ax2+Ay2

by putting values

A = √(-2.3cm)2+(4.1cm)2√(−2.3cm)2+(4.1cm)2

A = √5.29cm²+116.81cm²

A = √22.1cm²

A = 4.7 cm ------------Ans. 1

Now for direction, we have
Ax = -ve and Ay = +ve So,  →A lies  in 2nd quadrant, Thus the formula for  θ will be

θ = 180° - tan⁻¹(AyAx)

θ = 180° - tan⁻¹( 4.1cm2.3cm)

θ = 180° - tan⁻¹(-1.783)

θ = 180° - 60.7° 

θ = 119.3° -------------Ans. 2



(b)  →Ax = +3.9 cm,  →Ay = -1.8 cm


The formula to find the magnitude of vector A from its x and y component is 

A  = √Ax2+Ay2

by putting values

A = √(+3.9cm)2+(-1.8cm)2

A = √15.21cm²+3.24cm²

A = √18.45cm²

A = 4.3 cm ------------Ans. 1


Now for direction, we have
Ax = +ve and Ay = -ve So,  →A lies  in 4nd quadrant, Thus the formula for  θ will be

θ = 360° - tan⁻¹(AyAx)

θ = 360° - tan⁻¹( 1.8cm3.9cm)

θ = 360° - tan⁻¹(0.462)

θ = 360° - 24.8° 

θ = 335.2° -------------Ans. 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.