Since a is perpendicular to b, their dot product is zero:
a⋅b=0
Given:
a=(sinθ)i^+(cosθ)j^
b=i^−3j^
Taking the dot product:
(sinθ)(1)+(cosθ)(−3)=0
sinθ−3cosθ=0
sinθ=3cosθ
tanθ=3
Since θ is an acute angle:
θ=3π
If θ is an acute angle and the vector a=(sinθ)i+(cosθ)j is perpendicular to the vector b=i−3j then θ is equal to
Held on 13 May 2025 · Verified 13 Jul 2026.
6π
3π
4π
2π
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