Question

Two Vectors of Magnitudes 4 units and 6 units act of 60°
with each other. What is the resuhant magnitude​

Answer 1

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Given :- }}}$

$\sf\implies Two \ vectors \ have \ magnitude \ 4 \ units \ \& \ 6\ units. \\\sf\implies They \ are \ acting \ at \ 60^{\circ}.$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: To \ Find :- }}}$

$\sf\implies The \ resultant \ magnitude$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Answer :- }}}$

The magnitude of given two vectors are 4 units and 6 units and they act at an angle of 60 ° . So the Resultant will be ,

$\green{\sf: \implies Resultant = \sqrt{ A^2 + B^2 + 2AB cos\theta}} \\\\\sf:\implies R = \sqrt{ 4^2 + 6^2 + 2(4)(6) cos60^{\circ}}\\\\\sf:\implies R = \sqrt{ 16 + 36 + 48 \times \dfrac{1}{2} } \\\\\sf:\implies R = \sqrt{ 52 + 24 }\\\\\sf:\implies R = \sqrt{ 76 } \\\\\sf:\implies R =\sqrt{ 4 \times 19 }\\\\\underline{\boxed{\red{\sf \implies Resultant = 2\sqrt{19} \ units .}}}$

$\boxed{\pink{\bf Hence \ the \ Resultant \ magnitude \ is \ 2 \sqrt{19}\ units }}$