Question

6.
If a+b+c=0(null vector, zero vector)
and |a|= 3 |b|= 5 and |c|= 7
then
Find angle between directions
of a and b (Ans: 60° )

Answer 1

Answer:

3π

Explanation:

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=21=cos60∘

⇒θ=3π