Question

a=i+3j-2k and b=2i+k then angle between 2a+band b is

Answer 1

a

=

i

^

+2

j

^

+2

k

^

b

=

1

^

−2

j

^

+2

k

^

We know,

dot product,

a

.

b

=∣

a

∣

∣

∣

∣

∣

b

∣

∣

∣

∣

cosθ

⇒cosθ=

∣

a

∣

∣

∣

∣

∣

b

∣

∣

∣

∣

a

.

b

⟶(1)

a

.

b

=1−4+4=1

∣

a

∣=

1

2

+2

2

+2

2

=3

∣

∣

∣

∣

b

∣

∣

∣

∣

=

1

2

+2

2

+2

2

=3

Using (1),

⇒cosθ=

3.3

1

=

9

1

⇒cosθ=

9

1

⇒θ=cos

−1

9

1