Question

two vectors A and B of magnitude 5 units and 7 units respectively make an angle 60 degree with each other as shown below find the magnitude of the resultant vector and its direction with respect to the vectorA?​

Answer 1

Answer : resultant=√5^2+7^2+2×5×7cos60=

√25+49+70×1/2=

√74+35=

√109

Direction tan beta=bsin threta/a+bcosthreta=

7sin60/5+7cos60

7√3/2÷ 5+7×1/2

3.5√3/8.5

0.71

Answer 2

Two vectors A and B of magnitude 5 units and 7 units respectively make an angle 60° with each other as shown below.

We have to find the magnitude of the resultant vector and its direction with respect to the vector A.

We know, the resultant of two vectors A and B is given by,

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

here, A = 5 units , B = 7 units , θ = 60°

$R=\sqrt{5^2+7^2+2(5)(7)cos60^{\circ}}$

$=\sqrt{25+49+70\times\frac{1}{2}}$

$=\sqrt{25+49+35}$

$=\sqrt{109}$

Therefore the resultant of A and B is √(109)

let Ф is the angle made by vector R with vector A.

$tan\Phi=\left(\frac{Bsin\theta}{A+Bcos\theta}\right)$

$=\left(\frac{7sin60^{\circ}}{5+7cos60^{\circ}}\right)$

= 0.713

⇒ Ф = tan⁻¹(0.713) = 35.5°

Therefore the angle made by resultant R with A is 35.5°