Question

If the vectors a b and b have magnitudes 8 15 and 17 and a+b=c

Answer 1

Question given is incomplete. Complete Question will be If the vectors a b and b have magnitudes 8 15 and 17 and a+b=c.Find the angle between a and b.

Solutions ⇒
Let θ be the angles between the vectors a and b.

 Given condition ⇒
Magnitude of the Vector a = 8 units.
Magnitude of the Vectors b = 15 units.
Magnitude of the Vectors c = 17 units.

Now,
 The magnitudes of a, b and c can be written as ⇒

|a|² + |b|² + |a||b| Cos θ = |c|²
∴ |8|² + |15|² + |8||15| Cos θ = |17|²
⇒ 64 + 225 + 120 Cos θ = 289
⇒ 289 + 120 Cos θ = 289
⇒ 120 Cos θ = 289 - 289
⇒ 120 Cos θ = 0
∴ Cos θ = 0/120
∴ Cos θ = 0
⇒ Cos θ = Cos 90°
On comparing,
   θ = 90°


Hence, the angle between the vectors a and b is 90°.


Hope it helps.

Answer 2

The further part of the question must be find the angle between Vector (A)
and Vector (B)
So,
Vector (A)=8
Vector (B)=15
Vector (C)=17

Also
Mod(A)+Mod(B)=Mod(c)

So by the laws of vector addition
√(a² +b² +ab cosФ ) =c
Where a,b,c represent magnitude of the vectors
and Ф represents angle between the two vectors
So,
(a² +b² +ab cosФ ) =c²
We know that,
a=8 b=15 c=17
So,
8²+15² +8*15* cosФ =17²
64+225 +120* cosФ =289
So,
120* cosФ=289-289
120* cosФ=0
 cosФ =0
 Ф=90°
So the angle between the two vectors is 90° degrees