Question

Find the angle between two vectors a=2i+j-k and b=i+j

Answer 1

Answer:

Angle between vectors A and B is cos(theta) A.B/|A||B|

A•B=2×1+(-1×-1)=2+1=3

|A|=√6,|B|=√2

Cos(theta)=3/√2√6=3/√12=3/2√3=√3/2

cos(theta)=√3/2=cos30°

Therefore angle between the vectors is 30°

Answer 2

Answer:

cos⁻¹ ( √ 12 / 4 )

Explanation:

Given :

A = 2 i + j + k

B = i + j

We have to angle between them ( Ф ) :

Using dot product :

A . B = A B cos Ф

cos Ф = ( A . B ) / ( | A | . | B | )

cos Ф = [ ( 2 i + j + k ) . ( i + j ) ] / [ √ ( 2² + 1² + ( - 1 )² ) . √ ( 1² + 1² ) ]

cos Ф = [ ( 2 + 1 ) ] / [ √ ( 6 ) . √ 2 ]

cos Ф = 3 / √ 12

cos Ф = 3 √ 12 / 12

cos Ф = √ 12 / 4

Ф = cos⁻¹ ( √ 12 / 4 )

Hence we get required answer!