Question

(a) R = 25 units and tan ϕ = 4/3
(b) R = 5 units and tan ϕ = 4/3
(c) R = 25 units and tan ϕ = 3/4
(d) R = 5 units and tan ϕ = 3/4​

Answer 1

(a)

hope it helps you

than you

Answer 2

$\vec{A}$ = 3 units and $\vec{B}$ = 4 units. And the vectors are at an angle 90°.

So, resultant vector will be :

$R = \sqrt{ {A}^{2} + {B}^{2} + 2AB \cos( \theta) }$

$\implies R = \sqrt{ {A}^{2} + {B}^{2} + 2AB \cos( {90}^{ \circ} ) }$

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

$\implies R = \sqrt{ {3}^{2} + {4}^{2} }$

$\implies R = \sqrt{ 16 + 9 }$

$\implies R = \sqrt{ 25 }$

$\implies R = 5 \: unit$

Now, we can say:

$\tan( \phi) = \dfrac{ |B| }{ |A| }$

$\implies\tan( \phi) = \dfrac{ 4 }{ 3 }$

Hope It Helps.