Question

Find the angle between (i-j) hat and (j+k)hat

Answer 1

Answer:

• duyfjugfjyrcy5evrgfgtrbgf5b4td3yhtj

Answer 2

Answer:

Your question is actually ambiguous about the magnitude of the vectors involved, but fortunately, that doesn’t change the final answer

Interpretation 1: What is the angle between i^+j^ and j^+k^ ?

Interpretation 2: What is the angle between i+jˆ and j+kˆ ?

Interpretation 1 is more straightforward, so let’s use that. To find the angle between two vectors, we can use this property of the dot product of two vectors a and b:

a⋅b=∥a∥∥b∥cosθ

For your two vectors, this becomes:

(i^+j^)⋅(j^+k^)=∥i^+j^∥∥j^+k^∥cosθ

⟹(1)(0)+(1)(1)+(0)(1)=(12+12−−−−−−√)(12+12−−−−−−√)cosθ

⟹1=2–√2–√cosθ

⟹1=2cosθ

⟹12=cosθ

⟹θ=cos−1(12)

⟹θ=60°=π3 radians