Question

Find the angle between unit vector I and a=√3i+j
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Answer 1

Recall that for two vectors x and y,

x • y = ||x|| ||y|| cos(θ)

where θ is the angle between them.

We have

i • (√3 i + j) = √3

||i|| = 1

||√3 i + j|| = √((√3)² + 1²) = √4 = 2

Solve for θ :

√3 = 2 cos(θ)

cos(θ) = √3/2

θ = arccos(√3/2) = π/6

(Note that we assume θ is the acute angle between the vectors.)