Question

If teta is the angle between the vector ibar+jbar and jbar+kbar then find sin teta

Answer 1

Step-by-step explanation:

Let the given vectors are

a

=

i

^

−2

j

^

+3

k

^

and

b

=3

i

^

−2

j

^

+

k

^

∣

a

∣=

1

2

+(−2)

2

+3

2

=

1+4+9

=

14

∣

∣

∣

∣

b

∣

∣

∣

∣

=

3

2

+(−2)

2

+1

2

=

9+4+1

=

14

Now,

a

⋅

b

=(

i

^

−2

j

^

+3

k

^

)(3

i

^

−2

j

^

+

k

^

)

=1.3+(−2)(−2)+3.1

=3+4+3=10

Also, we know that

a

⋅

b

=∣

a

∣∣

b

∣cosθ

∴10=

14

14

cosθ

⇒cosθ=

14

10

⇒θ=cos

−1

(

7

5

)