Question

44. If (vector) A+B = C and A+B=C, then the angle between
A and C is

(1) 0
(3)
TT
(4)
4
2​

Answer 1

Answer:

The answer is given with the

Explanation:

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.