Question

The angle bw two vectors (I cap + j cap) and ( j cap + k cap) is:

Answer 1

Hello,

Let

a^ =I cap + j cap

b^ =j cap + k cap, Be two vectors

We know that,

Dot product of two vectors is,

a.b=|a||b|cos(a, b)

From this,

cos(a, b) =a.b/(|a||b|)

a.b=(I cap + j cap).(j cap + k cap)

=1

|a|=sqrt(1^2+1^2)

=sqrt(2)

|b|=sqrt(1^2+1^2)

=sqrt(2)

Now,

cos(a, b) =a.b/(|a||b|)

=1/sqrt(2) ^2

=1/2

Angle between the two vectors is given by the inverse of cosine function.

Angle =Cos^-1(1/2)

= 60°

I hope this is clear!