The angles of a triangle

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The angles of a triangle, two of whose sides are represented by vectors

\sqrt{3}(\hat{\boldsymbol{a}} \times \hat{\boldsymbol{b}})

and

\hat{\boldsymbol{b}} - (\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{a}}

, where

\hat{\boldsymbol{b}}

is a non-zero vector and

\hat{\boldsymbol{a}}

is a unit vector in the direction of

\boldsymbol{a}

, are (1)

\tan^{-1}(\sqrt{3})

(2)

\tan^{-1}(1/\sqrt{3})

(3)

\cot^{-1}(0)

(4)

\tan^{-1}(1)