Question

If |a|=2, |b|=5 and a•b=8 then |a+b|=?​

Answer 1

Given that

∣

a

ˉ

∣=2,∣

b

ˉ

∣=5

∣

a

ˉ

×

b

ˉ

∣=8

Consider ∣

a

ˉ

×

b

ˉ

∣=∣

a

ˉ

∣⋅∣

b

ˉ

∣⋅sinθ

⇒8=2⋅5sinθ

⇒

10

8

=sinθ

sinθ=

5

4

θ=sin

−1

(

5

4

)

a

ˉ

⋅

b

ˉ

=∣

a

ˉ

∣⋅∣

b

ˉ

∣cosθ

=2⋅5cos[sin

−1

(

5

4

)]

=10cos[cos

−1

(

5

3

)]

=10×

5

3

=6

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