Question

the maximum and minimum numerical value of the resultant of two vectors are respectively 20 and 16 units find the magnitude of individual vectors​

Answer 1

Answer:

${\huge{\pink{↬}}} \:  \: {\huge{\underline{\boxed{\bf{\pink{Answer}}}}}}$

Step 1: Equation for resultant of two vectors

Let θ be the angle between the vectors A and B

The resultant of two vectors is given by

                 R=A2+B2+2ABcosθ

For Rmax,θ=0∘

        ⇒∣Rmax∣=∣A∣+∣B∣

        ⇒17=∣A∣+∣B∣                                                                                                            ....(1)    

For Rmin,θ=180∘

        ⇒∣Rmin∣=∣A∣−∣B∣

        ⇒7=∣A∣−∣B∣                                                                                                              ....(2)   

 

Step 2: Calculation of Magnitude of A and B

                 

Adding equation (1) and (2)       ⇒2∣A∣=24 

                                                      

Answer 2

""" ❤️ Answer ❤️ """

Step 1: Equation for resultant of two vectors

Letθbe the angle between the vectors

A

and

B

The resultant of two vectors is given by

R=

2

A 2

For

R

max

,θ=

0 ∘

⇒

∣

R

max

∣=

∣ A ∣+

∣ B ∣

⇒ 17=

∣ A ∣+

∣ B ∣

....(1)

For

R

min

,θ=

180

∘

⇒

∣

R

min

∣=

∣ A ∣−

∣ B ∣

⇒

7=

∣ A ∣−

∣ B ∣

....(2)

Step 2: Calculation of Magnitude of A and B

⇒

Adding equation (1) and

(2)

2∣ A ∣=

24

⇒

A =

12

From equation (1)⇒

∣ B ∣=

5

Step 3: Calculation of R when vectors are perpendicular

∵

A⊥B

∣ R ∣=

2

o

A 2

⇒

∣ R ∣=

12

2

+5

2

=

169

units

⇒

∣ R ∣=

13

units

Hence the magnitude of resultant vector is 13units. Option

D

is correct