Question

If a + b + c = 0 and a = 3, b= 4 and c= 5, then a . b + b c + c . a is (1) - 15 (2) 15 (3) - 25 (4) 25​

Answer 1

Answer:

Correct option is

B

3

π

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