Question

There are three non zero vectors a ^-> , b^->,c^-> .
they are related as vector(a + b ) = vector c. and a + b = c. show that vector a and b are parallel. ​

Answer 1

Reason:

since angle between vector a and vector b is 0° so,

they are parallel

Explanation:

given that,

there are three non zero vectors,

vector a,  b and c

and also given that,

vector c is equal to the sum of both vectors.

i.e.

a^-> + b^-> = c^-> = R

and also given,

magnitude of c is equal to the sum of

magnitude of a and b

i.e.

a + b = c

now,

R = √(a² + b² + 2ab cosθ)

|a^-> + b^->| = √(a² + b² + 2ab cosθ)

a + b = √(a² + b² + 2ab cosθ)

squaring both sides

(a + b)² = a² + b² + 2ab cosθ

a² + b² + 2ab = a² + b² + 2ab cosθ

2ab = 2ab cosθ

cosθ = 2ab/2ab

cosθ = 1

so,

θ = 0°

and we know that,

when the angle between two lines is 0° then the two lines are parallel

so,

vector a and b are parallel

Answer 2

Explanation:

angle between vectors are 0° so a and b are parallel

see the attached file

Refer to attachment