Question

Two vector A and B both are 10 unit making angle of 30* and 60* with x-axis the magnitude of resultantwhich componants is larger

Answer 1

Solution :-

◾As given

▪️Vector A = 10 unit

▪️Angle with x-axis = 30°

▪️Vector B = 10 unit

▪️Angle with x axis = 60°

◾Now resolving vector A

➡️X component :-

= 10 cos30°

= 10 × √3/2

= 5√3

➡️Y component :-

= 10 sin30°

= 10 × 1/2

= 5

◾Now resolving vector B

➡️X component

= 10 Cos60°

= 10 × 1/2

= 5

➡️Y component

= 10 sin60°

= 10 × √3/2

= 5√3

◾Now

▪️Total X component = 5√3 + 5

▪️Total Y component = 5 + 5√3

◾Now Resultant of vectors :-

$\vec{R} = \sqrt{X^2 + Y^2}$

$\vec{R} = \sqrt{ ( 5 + 5\sqrt{3})^2 +( 5 + 5\sqrt{3})^2}$

$\vec{R} = \sqrt{2\times( 5 + 5\sqrt{3})^2}$

$\vec{R} = ( 5 + 5\sqrt{3})\sqrt{2}$

$\vec{R} = 5\sqrt{2}(1+\sqrt{3})$