Question

In the given figure what is the value of $\overrightarrow{ \sf F \ }$ in terms of the other vectors, if all the vectors lie along the sides of a regular hexagon?

Grade 11, Physics.

Answer 1

To Find:

Value of vector F in terms of other vectors

Diagram:

(See the first attachment)

Solution:

With the help of diagram,

On applying triangle law of vector addition on vectors E, D and M, we get

$\longrightarrow\rm{\vec{M}=\vec{D}+\vec{E}}------(1)$

On applying triangle law of vector addition on vectors A, B and O, we get

$\longrightarrow\rm{\vec{O}=\vec{A}+\vec{B}}------(2)$

$\rule{190}{1}$

Now, on applying triangle law of vector addition on vectors N, O and C, we get

$\longrightarrow\rm{\vec{C}=\vec{N}+\vec{O}}$

$\longrightarrow\rm{\vec{C}-\vec{O}=\vec{N}}$

$\longrightarrow\rm{\vec{N}=\vec{C}-\vec{O}}------(3)$

$\rule{190}{1}$

Now, on applying triangle law of vector addition on vectors N, F and M, we get

$\longrightarrow\rm{\vec{M}=\vec{N}+\vec{F}}$

$\longrightarrow\rm{\vec{M}-\vec{N}=\vec{F}}$

$\longrightarrow\rm{\vec{F}=\vec{M}-\vec{N}}$

From (1) and (3), we get

$\longrightarrow\rm{\vec{F}=\vec{D}+\vec{E}-(\vec{C}-\vec{O})}$

$\longrightarrow\rm{\vec{F}=\vec{D}+\vec{E}-\vec{C}+\vec{O}}$

From (2), we get

$\longrightarrow\rm{\vec{F}=\vec{D}+\vec{E}-\vec{C}+\vec{A}+\vec{B}}$

or

$\longrightarrow\rm\green{\vec{F}=\vec{A}+\vec{B}-\vec{C}+\vec{D}+\vec{E}}$

$\rule{190}{1}$

Triangle Law of Vector Addition

If two vectors A and B lies along two consecutive sides of triangle with Head to tail position, then the third vector R taken opposite in order represents the third side of triangle and is equal to the sum of other two vectors.

i.e R=A+B

(See the diagram provided in second attachment)

Answer 2

$see in attachment$