Question

find the angle between A(vector) and B(vector) given c=b/2

Answer 1

Given that
$c = \frac{b}{2} \\ \frac{c}{b} = \frac{1}{2} = \sin(30)$
Thus, the angle between b and a is 30 degrees.
^_^

Answer 2

yuThank you for A2A.

This is a question which I loved while answering. Thank you for giving me an opportunity to answer this one.

We have,

a+b=c ……………………(1)

Also,

|a|+|b|=|c| …………(2)

Square the equation, (1), we get,

(a+b).(a+b)=c.c

Implies,

|a|2+|b|2|+2(a.b)=|c|2 ……….(3)

From (2), we can get,

|a|2+|b|2|+2|a||b|=|c|2 ………(4)

Since the RHS’s of (3) and (4) are same, we can equate them, we get,

|a|2+|b|2|+2(a.b)=|a|2+|b|2|+2|a||b|

Implies,

a.b=|a||b|

Dot Product of 2 vectors is the product of absolute values of the vectors with the cosine of angle between them. So,

|a||b|cosx=|a||b|

Here, x is the angle between a and b.

So,

cosx=1

Take cosine inverse or arccos on both sides, we get,

x=cos−1(1)

Implies,

x=0

So, the angle between the 2 given vectors is 0, which means they’re parallel.

I hope my answer was helpful. If you’ve any questions regarding Mathematics, Physics or Computers, ask me.

Good day my math learning friend!!!

Once again, thank you for A2A.