Question

the resultant of two vectors is perpendicular to one of them and angle between them is 120 has the magnitude of smaller vector is​

Answer 1

$\huge{\underline{\underline{\boxed{\sf{\purple{Answer : }}}}}}$

The representation of the vectors to the triangular geometry of vectors,bring the resultant as the perpendicular on the smaller base vector and the hypotenuse being the second component the larger vector(10 units) at 120° to the base one ie the opposite angle of side containing the resultant is (180–120)=60°.From the trigonometry of right∆,it can be got that the perpendicular/hypotenuse=sin(contained angle) = sin60°

= √3/2.

So resultant ie the perpendicular vector = 10×(√3/2)

=5,

the smaller vector being the base of the right

$\small \underline {\sf{∆ \ is \ hypotenuse ~ × \ cos60° \ = \ 10×(1/2) \ = \ 5units. }}$

Answer 2

The representation of the vectors to the triangular geometry of vectors,bring the resultant as the perpendicular on the smaller base vector and the hypotenuse being the second component the larger vector(10 units) at 120° to the base one ie the opposite angle of side containing the resultant is (180–120)=60°.From the trigonometry of right∆,it can be got that the perpendicular/hypotenuse=sin(contained angle) = sin60°

= √3/2.

So resultant ie the perpendicular vector = 10×(√3/2)

=5,

the smaller vector being the base of the right

\small \underline {\sf{∆ \ is \ hypotenuse ~ × \ cos60° \ = \ 10×(1/2) \ = \ 5units. }}

∆ is hypotenuse × cos60° = 10×(1/2) = 5units.