Question

the sum of three vectors shown in figure is zero then find magnitude of the vector OB. OC= 45° OA= 4 m

Answer 1

Given that,

OA = 4 m

Angle of OC = 45°

We need to calculate the magnitude of the vector OB and OC

Using diagram,

Firstly we write the component

$\vec{OA}=-4(j)$....(I)

$\vec{OB}=OB(i)$....(II)

$\vec{OC}=OC\cos(45)-i+OC\sin(45)j$......(III)

We know that.

The  sum of three vectors shown in figure is zero.

So, we add of these equations

$\vec{R}=\vec{OA}+\vec{OB}+\vec{OC}$

Put the value of OA, OB and OC

$0(i)+0(j)=-4(j)+OB(i)-OC\cos(45)i+OC\sin(45)j$

On comparing both sides

$-4+OC\times\dfrac{1}{\sqrt{2}}=0$....(IV)

$OB-OC\times\dfrac{1}{\sqrt{2}}=0$....(V)

From equation (IV)

$-4+OC\times\dfrac{1}{\sqrt{2}}=0$

$OC=4\sqrt{2}$

Put the value of OC in equation (V)

$OB-4\sqrt{2}\times\dfrac{1}{\sqrt{2}}=0$

$OB=4$

Hence, The magnitude of the vector OB and OC are 4 m and 4√2 m.

Answer 2

Given that,

OA = 4 m

Angle of OC = 45°

We need to calculate the magnitude of the vector OB and OC

Using diagram,

Firstly we write the component

$\vec{OA}=-4(j)$....(I)

$\vec{OB}=OB(i)$....(II)

$\vec{OC}=OC\cos(45)-i+OC\sin(45)j$......(III)

We know that.

The  sum of three vectors shown in figure is zero.

So, we add of these equations

$\vec{R}=\vec{OA}+\vec{OB}+\vec{OC}$

Put the value of OA, OB and OC

$0(i)+0(j)=-4(j)+OB(i)-OC\cos(45)i+OC\sin(45)j$

On comparing both sides

$-4+OC\times\dfrac{1}{\sqrt{2}}=0$....(IV)

$OB-OC\times\dfrac{1}{\sqrt{2}}=0$....(V)

From equation (IV)

$-4+OC\times\dfrac{1}{\sqrt{2}}=0$

$OC=4\sqrt{2}$

Put the value of OC in equation (V)

$OB-4\sqrt{2}\times\dfrac{1}{\sqrt{2}}=0$

$OB=4$

Hence, The magnitude of the vector OB and OC are 4 m and 4√2 m.

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