Question

if vector a + b is equal to c when a=3,b=4 and c=5 what is angle between a and c​

Answer 1

Answer:

Given, a+b+c=0

and ∣a∣=5,∣b∣=3,∣c∣=7

⇒a+b=c

On squaring both sides, we get

(a+b)

2

=(−c)

2

⇒∣a+b∣

2

=∣c∣

2

⇒∣a∣

2

+∣b∣

2

+2a⋅b=∣c∣

2

(∵θ be the angle between a and b)

⇒(5)

2

+(3)

2

+2∣a∣∣b∣cosθ=(7)

2

⇒25+9+2⋅5⋅3cosθ=49

⇒30cosθ=15

⇒cosθ=

2

1

=cos60

∘

⇒θ=

3

π