Question

the magnitude of vector a vector b vector and b vector are respecitively12 ,5and13 unit and a vector + b vector equal C vector then the angle between a vector and b vector is​

Answer 1

Answer:-

$\mathsf{\theta = 90^{\circ}}$

Given :-

$\vec{A}= 12\\ \vec{B}= 5 \\ \vec{C}= 13$

$\mathsf{ \vec{A} + \vec{B} = \vec{C}}$

To find :-

The angle between $\text{ \vec{A} and \vec{B} }$

Solution:-

• As we know the addition of two vector is given by formula.

$\mathsf{\vec{A}+\vec{B}= \sqrt{|\vec{A}|^2 +|\vec{B}|^2+ 2 |\vec{A}|.|\vec{B}|Cos \theta}}$

But,

$\mathsf{ \vec{A} + \vec{B} = \vec{C}}$

• Put the given values,

→$\mathsf{\vec{C} = \sqrt{(12)^2 + (5)^2 + 2 \times 12\times 5 Cos \theta}}$

→$\mathsf{|\vec{c}|= \sqrt{144 + 25 + 120 Cos \theta}}$

→$\mathsf{(13)^2 = 169 + 120 Cos \theta}$

→$\mathsf{ 169 = 169 + 120 Cos \theta}$

→$\mathsf{169-169 = 120 Cos \theta}$

→$\mathsf{0 = 120 Cos \theta}$

→$\mathsf{Cos \theta = \dfrac{0}{120}}$

→$\mathsf{Cos \theta = 0 }$

→$\mathsf{Cos \theta = Cos 90^{\circ}}$

• Cancelling out cos.

→$\mathsf{\theta = 90^{\circ}}$

hence,

The angle between $\vec{A}$ and $\vec{B}$ is 90°

Answer 2

see this attachment