Question

Two vectors having magnitude 8 and 10 can have maximum and minimum values of resultant

Answer 1

Hey mate!!!^_^

here is ur ans⭐⭐
________
________

Maximum is 18
and Minimum is 2

when they both act parallely the the angle b/w them is 0°and
when they act in opposite direction then the angle b/w them is 180°

Hope thsi helps u ^_^

⭐⭐⭐❤❤❤

mark it as brainliest ^_^

Answer 2

Given,

Value of first vector $A = 8 units$

value of second vector $B = 10 units$

Resultant of two vectors is given by,

$R = \sqrt{A^2+B^2+2ABcos\theta}$

Now,

1) Condition for maximum value of resultant: This occurs when the angle between the two vectors is $0$°. i.e $\theta = 0$° then,

$R_{max} = \sqrt{A^2+B^2+2ABcos0}$

we know that $cos0 =1$

$R_{max}= \sqrt{8^2+10^2+(2*8*10*1)} \\R_{max} = \sqrt{64+100+160} \\R_{max} = \sqrt{324} \\R_{max} = 18units$

2) Condition for minimum value of resultant: This occurs when the angle between the two vectors is $180$°. i.e $\theta = 180$° then,

$R_{min} = \sqrt{A^2+B^2+(2ABcos180)}$

we know that $cos180= -1$

$R_{min} = \sqrt{8^2+10^2+(2*8*10*(-1))} \\R_{min} = \sqrt{64+100-160} \\R_{min}=\sqrt{4}\\ R_{min} = 2units$

∴The maximum value of resultant is  $R_{max} = 18units$

  The minimum value of resultant is $R_{min} = 2units$

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