Question

let a and b be two given vectors such that |a| =2 and |b|= 1 and a×b=1 the angle between a and b is​

Answer 1

Step-by-step explanation:

Given ∣

a

∣=1,

∣

∣

∣

∣

b

∣

∣

∣

∣

=4

a

.

b

=2 and

c

=(2

a

×

b

)−3

b

a

.

b

=2⇒∣a∣∣b∣.cos(a,b)=2

1×4×cosθ=2

cosθ=

2

1

⇒θ=60

∘

(Angle b/w

a

,

b

)

a

×

b

=∣a∣∣b∣.sinθ=1×4×sin60=4×

2

2

=2

3

Given

c

=2

a

×

b

−3

b

squaring on both sides

∣

c

∣

2

=

∣

∣

∣

2

a

ˉ

×

b

ˉ

∣

∣

∣

2

+9

∣

∣

∣

∣

b

∣

∣

∣

∣

2

−2×(3

a

(2

a

×

b

))

∣

c

∣

2

=4

∣

∣

∣

∣

a

×

b

∣

∣

∣

∣

2

+9

∣

∣

∣

∣

b

∣

∣

∣

∣

2

−0

(∵

b

,2

a

×

b

are perpendicular to each other)

∣

c

∣

2

=4×(2

3

)

2

+9(4)

2

∣c∣

2

=4×12+9×16=48+144=192

∣c∣

2

=192⇒

∣c∣=8

3

c

=(2

a

×

b

)−3

b

dot product on both sides with

b

c

.

b

=(2

a

×

b

).

b

−3

b

.

b

c

.

b

=0−3∣b∣

2

(∵

b

12

a

×

b

and cos90=0)

∴∣c∣.∣b∣.cos(α)=−3∣b∣

cos(α)=

8

3

−3×4

=

2

−

3

−α=

6

5π