Question

if i cap , jcap and kcap represents unit vectors along the x , y ,and z axis then find the angle between i cap + jcap +k cap and i cap +j cap

Answer 1

We know from the dot product rule that ,

A.B = |A| |B| cosФ

So,

cosФ = (A.B) /(|A| |B|)

cosФ = (( i + j + k).(j +k))/ (√3 ×√2)

cosФ = 2/(√6)

So,

Ф = cos inverse of (2 /√6)

This will be the required angle between the vectors